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Enterprise Risk Management Case Studies: Heroes and Zeros

By Andy Marker | April 7, 2021

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We’ve compiled more than 20 case studies of enterprise risk management programs that illustrate how companies can prevent significant losses yet take risks with more confidence.   

Included on this page, you’ll find case studies and examples by industry , case studies of major risk scenarios (and company responses), and examples of ERM successes and failures .

Enterprise Risk Management Examples and Case Studies

With enterprise risk management (ERM) , companies assess potential risks that could derail strategic objectives and implement measures to minimize or avoid those risks. You can analyze examples (or case studies) of enterprise risk management to better understand the concept and how to properly execute it.

The collection of examples and case studies on this page illustrates common risk management scenarios by industry, principle, and degree of success. For a basic overview of enterprise risk management, including major types of risks, how to develop policies, and how to identify key risk indicators (KRIs), read “ Enterprise Risk Management 101: Programs, Frameworks, and Advice from Experts .”

Enterprise Risk Management Framework Examples

An enterprise risk management framework is a system by which you assess and mitigate potential risks. The framework varies by industry, but most include roles and responsibilities, a methodology for risk identification, a risk appetite statement, risk prioritization, mitigation strategies, and monitoring and reporting.

To learn more about enterprise risk management and find examples of different frameworks, read our “ Ultimate Guide to Enterprise Risk Management .”

Enterprise Risk Management Examples and Case Studies by Industry

Though every firm faces unique risks, those in the same industry often share similar risks. By understanding industry-wide common risks, you can create and implement response plans that offer your firm a competitive advantage.

Enterprise Risk Management Example in Banking

Toronto-headquartered TD Bank organizes its risk management around two pillars: a risk management framework and risk appetite statement. The enterprise risk framework defines the risks the bank faces and lays out risk management practices to identify, assess, and control risk. The risk appetite statement outlines the bank’s willingness to take on risk to achieve its growth objectives. Both pillars are overseen by the risk committee of the company’s board of directors.  

Risk management frameworks were an important part of the International Organization for Standardization’s 31000 standard when it was first written in 2009 and have been updated since then. The standards provide universal guidelines for risk management programs.  

Risk management frameworks also resulted from the efforts of the Committee of Sponsoring Organizations of the Treadway Commission (COSO). The group was formed to fight corporate fraud and included risk management as a dimension. 

Once TD completes the ERM framework, the bank moves onto the risk appetite statement. 

The bank, which built a large U.S. presence through major acquisitions, determined that it will only take on risks that meet the following three criteria:

• The risk fits the company’s strategy, and TD can understand and manage those risks. 
• The risk does not render the bank vulnerable to significant loss from a single risk.
• The risk does not expose the company to potential harm to its brand and reputation. 

Some of the major risks the bank faces include strategic risk, credit risk, market risk, liquidity risk, operational risk, insurance risk, capital adequacy risk, regulator risk, and reputation risk. Managers detail these categories in a risk inventory. 

The risk framework and appetite statement, which are tracked on a dashboard against metrics such as capital adequacy and credit risk, are reviewed annually. 

TD uses a three lines of defense (3LOD) strategy, an approach widely favored by ERM experts, to guard against risk. The three lines are as follows:

• A business unit and corporate policies that create controls, as well as manage and monitor risk
• Standards and governance that provide oversight and review of risks and compliance with the risk appetite and framework 
• Internal audits that provide independent checks and verification that risk-management procedures are effective

Enterprise Risk Management Example in Pharmaceuticals

Drug companies’ risks include threats around product quality and safety, regulatory action, and consumer trust. To avoid these risks, ERM experts emphasize the importance of making sure that strategic goals do not conflict. 

For Britain’s GlaxoSmithKline, such a conflict led to a breakdown in risk management, among other issues. In the early 2000s, the company was striving to increase sales and profitability while also ensuring safe and effective medicines. One risk the company faced was a failure to meet current good manufacturing practices (CGMP) at its plant in Cidra, Puerto Rico. 

CGMP includes implementing oversight and controls of manufacturing, as well as managing the risk and confirming the safety of raw materials and finished drug products. Noncompliance with CGMP can result in escalating consequences, ranging from warnings to recalls to criminal prosecution. 

GSK’s unit pleaded guilty and paid $750 million in 2010 to resolve U.S. charges related to drugs made at the Cidra plant, which the company later closed. A fired GSK quality manager alerted regulators and filed a whistleblower lawsuit in 2004. In announcing the consent decree, the U.S. Department of Justice said the plant had a history of bacterial contamination and multiple drugs created there in the early 2000s violated safety standards.

According to the whistleblower, GSK’s ERM process failed in several respects to act on signs of non-compliance with CGMP. The company received warning letters from the U.S. Food and Drug Administration in 2001 about the plant’s practices, but did not resolve the issues. 

Additionally, the company didn’t act on the quality manager’s compliance report, which advised GSK to close the plant for two weeks to fix the problems and notify the FDA. According to court filings, plant staff merely skimmed rejected products and sold them on the black market. They also scraped by hand the inside of an antibiotic tank to get more product and, in so doing, introduced bacteria into the product.

Enterprise Risk Management Example in Consumer Packaged Goods

Mars Inc., an international candy and food company, developed an ERM process. The company piloted and deployed the initiative through workshops with geographic, product, and functional teams from 2003 to 2012. 

Driven by a desire to frame risk as an opportunity and to work within the company’s decentralized structure, Mars created a process that asked participants to identify potential risks and vote on which had the highest probability. The teams listed risk mitigation steps, then ranked and color-coded them according to probability of success. 

Larry Warner, a Mars risk officer at the time, illustrated this process in a case study . An initiative to increase direct-to-consumer shipments by 12 percent was colored green, indicating a 75 percent or greater probability of achievement. The initiative to bring a new plant online by the end of Q3 was coded red, meaning less than a 50 percent probability of success. 

The company’s results were hurt by a surprise at an operating unit that resulted from a so-coded red risk identified in a unit workshop. Executives had agreed that some red risk profile was to be expected, but they decided that when a unit encountered a red issue, it must be communicated upward when first identified. This became a rule. 

This process led to the creation of an ERM dashboard that listed initiatives in priority order, with the profile of each risk faced in the quarter, the risk profile trend, and a comment column for a year-end view. 

According to Warner, the key factors of success for ERM at Mars are as follows:

• The initiative focused on achieving operational and strategic objectives rather than compliance, which refers to adhering to established rules and regulations.
• The program evolved, often based on requests from business units, and incorporated continuous improvement. 
• The ERM team did not overpromise. It set realistic objectives.
• The ERM team periodically surveyed business units, management teams, and board advisers.

Enterprise Risk Management Example in Retail

Walmart is the world’s biggest retailer. As such, the company understands that its risk makeup is complex, given the geographic spread of its operations and its large number of stores, vast supply chain, and high profile as an employer and buyer of goods. 

In the 1990s, the company sought a simplified strategy for assessing risk and created an enterprise risk management plan with five steps founded on these four questions:

• What are the risks?
• What are we going to do about them?
• How will we know if we are raising or decreasing risk?
• How will we show shareholder value?

The process follows these five steps:

• Risk Identification: Senior Walmart leaders meet in workshops to identify risks, which are then plotted on a graph of probability vs. impact. Doing so helps to prioritize the biggest risks. The executives then look at seven risk categories (both internal and external): legal/regulatory, political, business environment, strategic, operational, financial, and integrity. Many ERM pros use risk registers to evaluate and determine the priority of risks. You can download templates that help correlate risk probability and potential impact in “ Free Risk Register Templates .”
• Risk Mitigation: Teams that include operational staff in the relevant area meet. They use existing inventory procedures to address the risks and determine if the procedures are effective.
• Action Planning: A project team identifies and implements next steps over the several months to follow.
• Performance Metrics: The group develops metrics to measure the impact of the changes. They also look at trends of actual performance compared to goal over time.
• Return on Investment and Shareholder Value: In this step, the group assesses the changes’ impact on sales and expenses to determine if the moves improved shareholder value and ROI.

To develop your own risk management planning, you can download a customizable template in “ Risk Management Plan Templates .”

Enterprise Risk Management Example in Agriculture

United Grain Growers (UGG), a Canadian grain distributor that now is part of Glencore Ltd., was hailed as an ERM innovator and became the subject of business school case studies for its enterprise risk management program. This initiative addressed the risks associated with weather for its business. Crop volume drove UGG’s revenue and profits. 

In the late 1990s, UGG identified its major unaddressed risks. Using almost a century of data, risk analysts found that extreme weather events occurred 10 times as frequently as previously believed. The company worked with its insurance broker and the Swiss Re Group on a solution that added grain-volume risk (resulting from weather fluctuations) to its other insured risks, such as property and liability, in an integrated program. 

The result was insurance that protected grain-handling earnings, which comprised half of UGG’s gross profits. The greater financial stability significantly enhanced the firm’s ability to achieve its strategic objectives. 

Since then, the number and types of instruments to manage weather-related risks has multiplied rapidly. For example, over-the-counter derivatives, such as futures and options, began trading in 1997. The Chicago Mercantile Exchange now offers weather futures contracts on 12 U.S. and international cities. 

Weather derivatives are linked to climate factors such as rainfall or temperature, and they hedge different kinds of risks than do insurance. These risks are much more common (e.g., a cooler-than-normal summer) than the earthquakes and floods that insurance typically covers. And the holders of derivatives do not have to incur any damage to collect on them.

These weather-linked instruments have found a wider audience than anticipated, including retailers that worry about freak storms decimating Christmas sales, amusement park operators fearing rainy summers will keep crowds away, and energy companies needing to hedge demand for heating and cooling.

This area of ERM continues to evolve because weather and crop insurance are not enough to address all the risks that agriculture faces. Arbol, Inc. estimates that more than $1 trillion of agricultural risk is uninsured. As such, it is launching a blockchain-based platform that offers contracts (customized by location and risk parameters) with payouts based on weather data. These contracts can cover risks associated with niche crops and small growing areas.

Enterprise Risk Management Example in Insurance

Switzerland’s Zurich Insurance Group understands that risk is inherent for insurers and seeks to practice disciplined risk-taking, within a predetermined risk tolerance. 

The global insurer’s enterprise risk management framework aims to protect capital, liquidity, earnings, and reputation. Governance serves as the basis for risk management, and the framework lays out responsibilities for taking, managing, monitoring, and reporting risks. 

The company uses a proprietary process called Total Risk Profiling (TRP) to monitor internal and external risks to its strategy and financial plan. TRP assesses risk on the basis of severity and probability, and helps define and implement mitigating moves. 

Zurich’s risk appetite sets parameters for its tolerance within the goal of maintaining enough capital to achieve an AA rating from rating agencies. For this, the company uses its own Zurich economic capital model, referred to as Z-ECM. The model quantifies risk tolerance with a metric that assesses risk profile vs. risk tolerance. 

To maintain the AA rating, the company aims to hold capital between 100 and 120 percent of capital at risk. Above 140 percent is considered overcapitalized (therefore at risk of throttling growth), and under 90 percent is below risk tolerance (meaning the risk is too high). On either side of 100 to 120 percent (90 to 100 percent and 120 to 140 percent), the insurer considers taking mitigating action. 

Zurich’s assessment of risk and the nature of those risks play a major role in determining how much capital regulators require the business to hold. A popular tool to assess risk is the risk matrix, and you can find a variety of templates in “ Free, Customizable Risk Matrix Templates .”

In 2020, Zurich found that its biggest exposures were market risk, such as falling asset valuations and interest-rate risk; insurance risk, such as big payouts for covered customer losses, which it hedges through diversification and reinsurance; credit risk in assets it holds and receivables; and operational risks, such as internal process failures and external fraud.

Enterprise Risk Management Example in Technology

Financial software maker Intuit has strengthened its enterprise risk management through evolution, according to a case study by former Chief Risk Officer Janet Nasburg. 

The program is founded on the following five core principles:

• Use a common risk framework across the enterprise.
• Assess risks on an ongoing basis.
• Focus on the most important risks.
• Clearly define accountability for risk management.
• Commit to continuous improvement of performance measurement and monitoring. 

ERM programs grow according to a maturity model, and as capability rises, the shareholder value from risk management becomes more visible and important. 

The maturity phases include the following:

• Ad hoc risk management addresses a specific problem when it arises.
• Targeted or initial risk management approaches risks with multiple understandings of what constitutes risk and management occurs in silos. 
• Integrated or repeatable risk management puts in place an organization-wide framework for risk assessment and response. 
• Intelligent or managed risk management coordinates risk management across the business, using common tools. 
• Risk leadership incorporates risk management into strategic decision-making. 

Intuit emphasizes using key risk indicators (KRIs) to understand risks, along with key performance indicators (KPIs) to gauge the effectiveness of risk management. 

Early in its ERM journey, Intuit measured performance on risk management process participation and risk assessment impact. For participation, the targeted rate was 80 percent of executive management and business-line leaders. This helped benchmark risk awareness and current risk management, at a time when ERM at the company was not mature.

Conduct an annual risk assessment at corporate and business-line levels to plot risks, so the most likely and most impactful risks are graphed in the upper-right quadrant. Doing so focuses attention on these risks and helps business leaders understand the risk’s impact on performance toward strategic objectives. 

In the company’s second phase of ERM, Intuit turned its attention to building risk management capacity and sought to ensure that risk management activities addressed the most important risks. The company evaluated performance using color-coded status symbols (red, yellow, green) to indicate risk trend and progress on risk mitigation measures.

In its third phase, Intuit moved to actively monitoring the most important risks and ensuring that leaders modified their strategies to manage risks and take advantage of opportunities. An executive dashboard uses KRIs, KPIs, an overall risk rating, and red-yellow-green coding. The board of directors regularly reviews this dashboard.

Over this evolution, the company has moved from narrow, tactical risk management to holistic, strategic, and long-term ERM.

Enterprise Risk Management Case Studies by Principle

ERM veterans agree that in addition to KPIs and KRIs, other principles are equally important to follow. Below, you’ll find examples of enterprise risk management programs by principles.

ERM Principle #1: Make Sure Your Program Aligns with Your Values

Raytheon Case Study U.S. defense contractor Raytheon states that its highest priority is delivering on its commitment to provide ethical business practices and abide by anti-corruption laws.

Raytheon backs up this statement through its ERM program. Among other measures, the company performs an annual risk assessment for each function, including the anti-corruption group under the Chief Ethics and Compliance Officer. In addition, Raytheon asks 70 of its sites to perform an anti-corruption self-assessment each year to identify gaps and risks. From there, a compliance team tracks improvement actions. 

Every quarter, the company surveys 600 staff members who may face higher anti-corruption risks, such as the potential for bribes. The survey asks them to report any potential issues in the past quarter.

Also on a quarterly basis, the finance and internal controls teams review higher-risk profile payments, such as donations and gratuities to confirm accuracy and compliance. Oversight and compliance teams add other checks, and they update a risk-based audit plan continuously.

ERM Principle #2: Embrace Diversity to Reduce Risk

State Street Global Advisors Case Study In 2016, the asset management firm State Street Global Advisors introduced measures to increase gender diversity in its leadership as a way of reducing portfolio risk, among other goals. 

The company relied on research that showed that companies with more women senior managers had a better return on equity, reduced volatility, and fewer governance problems such as corruption and fraud. 

Among the initiatives was a campaign to influence companies where State Street had invested, in order to increase female membership on their boards. State Street also developed an investment product that tracks the performance of companies with the highest level of senior female leadership relative to peers in their sector. 

In 2020, the company announced some of the results of its effort. Among the 1,384 companies targeted by the firm, 681 added at least one female director.

ERM Principle #3: Do Not Overlook Resource Risks

Infosys Case Study India-based technology consulting company Infosys, which employees more than 240,000 people, has long recognized the risk of water shortages to its operations. 

India’s rapidly growing population and development has increased the risk of water scarcity. A 2020 report by the World Wide Fund for Nature said 30 cities in India faced the risk of severe water scarcity over the next three decades. 

Infosys has dozens of facilities in India and considers water to be a significant short-term risk. At its campuses, the company uses the water for cooking, drinking, cleaning, restrooms, landscaping, and cooling. Water shortages could halt Infosys operations and prevent it from completing customer projects and reaching its performance objectives. 

In an enterprise risk assessment example, Infosys’ ERM team conducts corporate water-risk assessments while sustainability teams produce detailed water-risk assessments for individual locations, according to a report by the World Business Council for Sustainable Development .

The company uses the COSO ERM framework to respond to the risks and decide whether to accept, avoid, reduce, or share these risks. The company uses root-cause analysis (which focuses on identifying underlying causes rather than symptoms) and the site assessments to plan steps to reduce risks. 

Infosys has implemented various water conservation measures, such as water-efficient fixtures and water recycling, rainwater collection and use, recharging aquifers, underground reservoirs to hold five days of water supply at locations, and smart-meter usage monitoring. Infosys’ ERM team tracks metrics for per-capita water consumption, along with rainfall data, availability and cost of water by tanker trucks, and water usage from external suppliers. 

In the 2020 fiscal year, the company reported a nearly 64 percent drop in per-capita water consumption by its workforce from the 2008 fiscal year. 

The business advantages of this risk management include an ability to open locations where water shortages may preclude competitors, and being able to maintain operations during water scarcity, protecting profitability.

ERM Principle #4: Fight Silos for Stronger Enterprise Risk Management

U.S. Government Case Study The terrorist attacks of September 11, 2001, revealed that the U.S. government’s then-current approach to managing intelligence was not adequate to address the threats — and, by extension, so was the government’s risk management procedure. Since the Cold War, sensitive information had been managed on a “need to know” basis that resulted in data silos. 

In the case of 9/11, this meant that different parts of the government knew some relevant intelligence that could have helped prevent the attacks. But no one had the opportunity to put the information together and see the whole picture. A congressional commission determined there were 10 lost operational opportunities to derail the plot. Silos existed between law enforcement and intelligence, as well as between and within agencies. 

After the attacks, the government moved toward greater information sharing and collaboration. Based on a task force’s recommendations, data moved from a centralized network to a distributed model, and social networking tools now allow colleagues throughout the government to connect. Staff began working across agency lines more often.

Enterprise Risk Management Examples by Scenario

While some scenarios are too unlikely to receive high-priority status, low-probability risks are still worth running through the ERM process. Robust risk management creates a culture and response capacity that better positions a company to deal with a crisis.

In the following enterprise risk examples, you will find scenarios and details of how organizations manage the risks they face.

Scenario: ERM and the Global Pandemic While most businesses do not have the resources to do in-depth ERM planning for the rare occurrence of a global pandemic, companies with a risk-aware culture will be at an advantage if a pandemic does hit. 

These businesses already have processes in place to escalate trouble signs for immediate attention and an ERM team or leader monitoring the threat environment. A strong ERM function gives clear and effective guidance that helps the company respond.

A report by Vodafone found that companies identified as “future ready” fared better in the COVID-19 pandemic. The attributes of future-ready businesses have a lot in common with those of companies that excel at ERM. These include viewing change as an opportunity; having detailed business strategies that are documented, funded, and measured; working to understand the forces that shape their environments; having roadmaps in place for technological transformation; and being able to react more quickly than competitors. 

Only about 20 percent of companies in the Vodafone study met the definition of “future ready.” But 54 percent of these firms had a fully developed and tested business continuity plan, compared to 30 percent of all businesses. And 82 percent felt their continuity plans worked well during the COVID-19 crisis. Nearly 50 percent of all businesses reported decreased profits, while 30 percent of future-ready organizations saw profits rise. 

Scenario: ERM and the Economic Crisis  The 2008 economic crisis in the United States resulted from the domino effect of rising interest rates, a collapse in housing prices, and a dramatic increase in foreclosures among mortgage borrowers with poor creditworthiness. This led to bank failures, a credit crunch, and layoffs, and the U.S. government had to rescue banks and other financial institutions to stabilize the financial system.

Some commentators said these events revealed the shortcomings of ERM because it did not prevent the banks’ mistakes or collapse. But Sim Segal, an ERM consultant and director of Columbia University’s ERM master’s degree program, analyzed how banks performed on 10 key ERM criteria. 

Segal says a risk-management program that incorporates all 10 criteria has these characteristics: 

• Risk management has an enterprise-wide scope.
• The program includes all risk categories: financial, operational, and strategic. 
• The focus is on the most important risks, not all possible risks. 
• Risk management is integrated across risk types.
• Aggregated metrics show risk exposure and appetite across the enterprise.
• Risk management incorporates decision-making, not just reporting.
• The effort balances risk and return management.
• There is a process for disclosure of risk.
• The program measures risk in terms of potential impact on company value.
• The focus of risk management is on the primary stakeholder, such as shareholders, rather than regulators or rating agencies.

In his book Corporate Value of Enterprise Risk Management , Segal concluded that most banks did not actually use ERM practices, which contributed to the financial crisis. He scored banks as failing on nine of the 10 criteria, only giving them a passing grade for focusing on the most important risks. 

Scenario: ERM and Technology Risk  The story of retailer Target’s failed expansion to Canada, where it shut down 133 loss-making stores in 2015, has been well documented. But one dimension that analysts have sometimes overlooked was Target’s handling of technology risk. 

A case study by Canadian Business magazine traced some of the biggest issues to software and data-quality problems that dramatically undermined the Canadian launch. 

As with other forms of ERM, technology risk management requires companies to ask what could go wrong, what the consequences would be, how they might prevent the risks, and how they should deal with the consequences. 

But with its technology plan for Canada, Target did not heed risk warning signs. 

In the United States, Target had custom systems for ordering products from vendors, processing items at warehouses, and distributing merchandise to stores quickly. But that software would need customization to work with the Canadian dollar, metric system, and French-language characters. 

Target decided to go with new ERP software on an aggressive two-year timeline. As Target began ordering products for the Canadian stores in 2012, problems arose. Some items did not fit into shipping containers or on store shelves, and information needed for customs agents to clear imported items was not correct in Target's system. 

Target found that its supply chain software data was full of errors. Product dimensions were in inches, not centimeters; height and width measurements were mixed up. An internal investigation showed that only about 30 percent of the data was accurate. 

In an attempt to fix these errors, Target merchandisers spent a week double-checking with vendors up to 80 data points for each of the retailer’s 75,000 products. They discovered that the dummy data entered into the software during setup had not been altered. To make any corrections, employees had to send the new information to an office in India where staff would enter it into the system. 

As the launch approached, the technology errors left the company vulnerable to stockouts, few people understood how the system worked, and the point-of-sale checkout system did not function correctly. Soon after stores opened in 2013, consumers began complaining about empty shelves. Meanwhile, Target Canada distribution centers overflowed due to excess ordering based on poor data fed into forecasting software. 

The rushed launch compounded problems because it did not allow the company enough time to find solutions or alternative technology. While the retailer fixed some issues by the end of 2014, it was too late. Target Canada filed for bankruptcy protection in early 2015. 

Scenario: ERM and Cybersecurity System hacks and data theft are major worries for companies. But as a relatively new field, cyber-risk management faces unique hurdles.

For example, risk managers and information security officers have difficulty quantifying the likelihood and business impact of a cybersecurity attack. The rise of cloud-based software exposes companies to third-party risks that make these projections even more difficult to calculate. 

As the field evolves, risk managers say it’s important for IT security officers to look beyond technical issues, such as the need to patch a vulnerability, and instead look more broadly at business impacts to make a cost benefit analysis of risk mitigation. Frameworks such as the Risk Management Framework for Information Systems and Organizations by the National Institute of Standards and Technology can help.  

Health insurer Aetna considers cybersecurity threats as a part of operational risk within its ERM framework and calculates a daily risk score, adjusted with changes in the cyberthreat landscape. 

Aetna studies threats from external actors by working through information sharing and analysis centers for the financial services and health industries. Aetna staff reverse-engineers malware to determine controls. The company says this type of activity helps ensure the resiliency of its business processes and greatly improves its ability to help protect member information.

For internal threats, Aetna uses models that compare current user behavior to past behavior and identify anomalies. (The company says it was the first organization to do this at scale across the enterprise.) Aetna gives staff permissions to networks and data based on what they need to perform their job. This segmentation restricts access to raw data and strengthens governance. 

Another risk initiative scans outgoing employee emails for code patterns, such as credit card or Social Security numbers. The system flags the email, and a security officer assesses it before the email is released.

Examples of Poor Enterprise Risk Management

Case studies of failed enterprise risk management often highlight mistakes that managers could and should have spotted — and corrected — before a full-blown crisis erupted. The focus of these examples is often on determining why that did not happen. 

ERM Case Study: General Motors

In 2014, General Motors recalled the first of what would become 29 million cars due to faulty ignition switches and paid compensation for 124 related deaths. GM knew of the problem for at least 10 years but did not act, the automaker later acknowledged. The company entered a deferred prosecution agreement and paid a $900 million penalty. 

Pointing to the length of time the company failed to disclose the safety problem, ERM specialists say it shows the problem did not reside with a single department. “Rather, it reflects a failure to properly manage risk,” wrote Steve Minsky, a writer on ERM and CEO of an ERM software company, in Risk Management magazine. 

“ERM is designed to keep all parties across the organization, from the front lines to the board to regulators, apprised of these kinds of problems as they become evident. Unfortunately, GM failed to implement such a program, ultimately leading to a tragic and costly scandal,” Minsky said.

Also in the auto sector, an enterprise risk management case study of Toyota looked at its problems with unintended acceleration of vehicles from 2002 to 2009. Several studies, including a case study by Carnegie Mellon University Professor Phil Koopman , blamed poor software design and company culture. A whistleblower later revealed a coverup by Toyota. The company paid more than $2.5 billion in fines and settlements.

ERM Case Study: Lululemon

In 2013, following customer complaints that its black yoga pants were too sheer, the athletic apparel maker recalled 17 percent of its inventory at a cost of $67 million. The company had previously identified risks related to fabric supply and quality. The CEO said the issue was inadequate testing. 

Analysts raised concerns about the company’s controls, including oversight of factories and product quality. A case study by Stanford University professors noted that Lululemon’s episode illustrated a common disconnect between identifying risks and being prepared to manage them when they materialize. Lululemon’s reporting and analysis of risks was also inadequate, especially as related to social media. In addition, the case study highlighted the need for a system to escalate risk-related issues to the board. 

ERM Case Study: Kodak 

Once an iconic brand, the photo film company failed for decades to act on the threat that digital photography posed to its business and eventually filed for bankruptcy in 2012. The company’s own research in 1981 found that digital photos could ultimately replace Kodak’s film technology and estimated it had 10 years to prepare. 

Unfortunately, Kodak did not prepare and stayed locked into the film paradigm. The board reinforced this course when in 1989 it chose as CEO a candidate who came from the film business over an executive interested in digital technology. 

Had the company acknowledged the risks and employed ERM strategies, it might have pursued a variety of strategies to remain successful. The company’s rival, Fuji Film, took the money it made from film and invested in new initiatives, some of which paid off. Kodak, on the other hand, kept investing in the old core business.

Case Studies of Successful Enterprise Risk Management

Successful enterprise risk management usually requires strong performance in multiple dimensions, and is therefore more likely to occur in organizations where ERM has matured. The following examples of enterprise risk management can be considered success stories. 

ERM Case Study: Statoil 

A major global oil producer, Statoil of Norway stands out for the way it practices ERM by looking at both downside risk and upside potential. Taking risks is vital in a business that depends on finding new oil reserves. 

According to a case study, the company developed its own framework founded on two basic goals: creating value and avoiding accidents.

The company aims to understand risks thoroughly, and unlike many ERM programs, Statoil maps risks on both the downside and upside. It graphs risk on probability vs. impact on pre-tax earnings, and it examines each risk from both positive and negative perspectives. 

For example, the case study cites a risk that the company assessed as having a 5 percent probability of a somewhat better-than-expected outcome but a 10 percent probability of a significant loss relative to forecast. In this case, the downside risk was greater than the upside potential.

ERM Case Study: Lego 

The Danish toy maker’s ERM evolved over the following four phases, according to a case study by one of the chief architects of its program:

• Traditional management of financial, operational, and other risks. Strategic risk management joined the ERM program in 2006. 
• The company added Monte Carlo simulations in 2008 to model financial performance volatility so that budgeting and financial processes could incorporate risk management. The technique is used in budget simulations, to assess risk in its credit portfolio, and to consolidate risk exposure. 
• Active risk and opportunity planning is part of making a business case for new projects before final decisions.
• The company prepares for uncertainty so that long-term strategies remain relevant and resilient under different scenarios. 

As part of its scenario modeling, Lego developed its PAPA (park, adapt, prepare, act) model. 

• Park: The company parks risks that occur slowly and have a low probability of happening, meaning it does not forget nor actively deal with them.
• Adapt: This response is for risks that evolve slowly and are certain or highly probable to occur. For example, a risk in this category is the changing nature of play and the evolution of buying power in different parts of the world. In this phase, the company adjusts, monitors the trend, and follows developments.
• Prepare: This category includes risks that have a low probability of occurring — but when they do, they emerge rapidly. These risks go into the ERM risk database with contingency plans, early warning indicators, and mitigation measures in place.
• Act: These are high-probability, fast-moving risks that must be acted upon to maintain strategy. For example, developments around connectivity, mobile devices, and online activity are in this category because of the rapid pace of change and the influence on the way children play. 

Lego views risk management as a way to better equip itself to take risks than its competitors. In the case study, the writer likens this approach to the need for the fastest race cars to have the best brakes and steering to achieve top speeds.

ERM Case Study: University of California 

The University of California, one of the biggest U.S. public university systems, introduced a new view of risk to its workforce when it implemented enterprise risk management in 2005. Previously, the function was merely seen as a compliance requirement.

ERM became a way to support the university’s mission of education and research, drawing on collaboration of the system’s employees across departments. “Our philosophy is, ‘Everyone is a risk manager,’” Erike Young, deputy director of ERM told Treasury and Risk magazine. “Anyone who’s in a management position technically manages some type of risk.”

The university faces a diverse set of risks, including cybersecurity, hospital liability, reduced government financial support, and earthquakes.  

The ERM department had to overhaul systems to create a unified view of risk because its information and processes were not linked. Software enabled both an organizational picture of risk and highly detailed drilldowns on individual risks. Risk managers also developed tools for risk assessment, risk ranking, and risk modeling. 

Better risk management has provided more than $100 million in annual cost savings and nearly $500 million in cost avoidance, according to UC officials. 

UC drives ERM with risk management departments at each of its 10 locations and leverages university subject matter experts to form multidisciplinary workgroups that develop process improvements.

APQC, a standards quality organization, recognized UC as a top global ERM practice organization, and the university system has won other awards. The university says in 2010 it was the first nonfinancial organization to win credit-rating agency recognition of its ERM program.

Examples of How Technology Is Transforming Enterprise Risk Management

Business intelligence software has propelled major progress in enterprise risk management because the technology enables risk managers to bring their information together, analyze it, and forecast how risk scenarios would impact their business.

ERM organizations are using computing and data-handling advancements such as blockchain for new innovations in strengthening risk management. Following are case studies of a few examples.

ERM Case Study: Bank of New York Mellon 

In 2021, the bank joined with Google Cloud to use machine learning and artificial intelligence to predict and reduce the risk that transactions in the $22 trillion U.S. Treasury market will fail to settle. Settlement failure means a buyer and seller do not exchange cash and securities by the close of business on the scheduled date. 

The party that fails to settle is assessed a daily financial penalty, and a high level of settlement failures can indicate market liquidity problems and rising risk. BNY says that, on average, about 2 percent of transactions fail to settle.

The bank trained models with millions of trades to consider every factor that could result in settlement failure. The service uses market-wide intraday trading metrics, trading velocity, scarcity indicators, volume, the number of trades settled per hour, seasonality, issuance patterns, and other signals. 

The bank said it predicts about 40 percent of settlement failures with 90 percent accuracy. But it also cautioned against overconfidence in the technology as the model continues to improve. 

AI-driven forecasting reduces risk for BNY clients in the Treasury market and saves costs. For example, a predictive view of settlement risks helps bond dealers more accurately manage their liquidity buffers, avoid penalties, optimize their funding sources, and offset the risks of failed settlements. In the long run, such forecasting tools could improve the health of the financial market. 

ERM Case Study: PwC

Consulting company PwC has leveraged a vast information storehouse known as a data lake to help its customers manage risk from suppliers.

A data lake stores both structured or unstructured information, meaning data in highly organized, standardized formats as well as unstandardized data. This means that everything from raw audio to credit card numbers can live in a data lake. 

Using techniques pioneered in national security, PwC built a risk data lake that integrates information from client companies, public databases, user devices, and industry sources. Algorithms find patterns that can signify unidentified risks.

One of PwC’s first uses of this data lake was a program to help companies uncover risks from their vendors and suppliers. Companies can violate laws, harm their reputations, suffer fraud, and risk their proprietary information by doing business with the wrong vendor. 

Today’s complex global supply chains mean companies may be several degrees removed from the source of this risk, which makes it hard to spot and mitigate. For example, a product made with outlawed child labor could be traded through several intermediaries before it reaches a retailer. 

PwC’s service helps companies recognize risk beyond their primary vendors and continue to monitor that risk over time as more information enters the data lake.

ERM Case Study: Financial Services

As analytics have become a pillar of forecasting and risk management for banks and other financial institutions, a new risk has emerged: model risk . This refers to the risk that machine-learning models will lead users to an unreliable understanding of risk or have unintended consequences.

For example, a 6 percent drop in the value of the British pound over the course of a few minutes in 2016 stemmed from currency trading algorithms that spiralled into a negative loop. A Twitter-reading program began an automated selling of the pound after comments by a French official, and other selling algorithms kicked in once the currency dropped below a certain level.

U.S. banking regulators are so concerned about model risk that the Federal Reserve set up a model validation council in 2012 to assess the models that banks use in running risk simulations for capital adequacy requirements. Regulators in Europe and elsewhere also require model validation.

A form of managing risk from a risk-management tool, model validation is an effort to reduce risk from machine learning. The technology-driven rise in modeling capacity has caused such models to proliferate, and banks can use hundreds of models to assess different risks. 

Model risk management can reduce rising costs for modeling by an estimated 20 to 30 percent by building a validation workflow, prioritizing models that are most important to business decisions, and implementing automation for testing and other tasks, according to McKinsey.

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Case Study – Earthquake Savings

Case Study – Excess Attention

Several years later, an employee of the client was involved in a catastrophic automobile accident while driving a leased auto; the injured parties sustained life-altering injuries. Although the claim is still in discovery and damages have not been awarded, the conservative outlook of this claim indicates that it will more than pierce the excess liability limits. Had Stockbridge not uncovered this issue, this client would have found themselves with only $1,000,000 in limit available for this claim, and they would have been responsible for any damages above this limit.

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Case Study – Risk Transfer in Action

The adamant position of the GC’s carrier along with an unresponsive and ineffective adjuster assigned by the client’s insurance carrier did not give much hope for a tender of this claim. Stockbridge persisted in supplying the GC’s carrier with the necessary documentation to counter any further denial, and was successful in having the client’s adjuster replaced.

By the end of 2015, the GC’s carrier continued to deny any tender, but the client’s new adjuster pushed for a declaratory judgement. In 2016, the tender was accepted, and the client’s insurance carrier reduced the claim reserve from $785,000 to $1.

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4 informative case studies to help guide reputational risk management.

Nir Kossovsky is CEO of Steel City Re, which mitigates the hazards of reputation risk with parametric reputation insurances, ESG insurances, and risk management advisory services.

Societal phenomena such as #MeToo, #opioidcrisis, #boycottNRA and #deleteFacebook are exposing inadequacies in risk and governance frameworks, and astute managers recognize the need to seek remedies.

What’s needed are systems and processes helping risk managers prepare to adapt and respond to culturally-linked perils that are outside the usual framework of 1 st  party, 3rd party and compliance risks. Notwithstanding the implications for mission creep, development of those systems to protect corporate reputation is something enterprise risk managers should embrace.

Confidence in a company’s ability to pursue its strategy is what motivates investors to risk capital, lenders to advance capital and employees to engage. Customers expect to be delighted by product and service experiences.

These stakeholders, implicitly or through covenants, expect risks to their expectations will be managed. In addition, in certain commercial sectors, regulators demand risk management with failures manifesting in fines, criminal charges and loss of business rights. It is therefore obvious that the economic benefits of meeting stakeholders’ expectations is the value of a firm’s reputation; the Economist newspaper crowned risk to that value as the “risk of risks” more than a decade ago.

Most risk management frameworks lump reputation among a firm’s valuable assets. Reputation risk, it would seem, should be managed like other 1st party risks. Actuarial models developed by risk bearers help risk managers allocate resources to mitigate 1st party economic losses. However, until my firm developed actuarial models for reputation risk using synthetic measures of reputation value, the insurance world offered little guidance.

What follows are four case studies on how company’s tried and failed or succeeded in managing this risk.

Example 1: Facebook.

Facebook’s 2017 10K explicitly notes the value of reputation and the potential cost of its loss 14 times. In the spring of 2018, the audit committee was overseeing reputational matters but had no quantitative measure of reputation’s importance and no risk managers working from a framework that linked reputation risk to cash flows or other economic metrics. As a result, few at Facebook seemed to anticipate that the loss of trust precipitated by the Cambridge Analytica disclosures would erase 20 percent of the firm’s market cap when its impact on user growth and engagement became known to investors.

Facebook created the expectation of trust and failed to meet it. Reputation risk is the peril of stakeholders’ disappointment and anger when there is a gap between stakeholder expectations and reality. Noxious media typically amplifies that gap, which it certainly did in Facebook’s case.

Liability risk models, such as the burden-probability-loss formula that was articulated in Judge Learned Hand’s 1947 ruling are failing in the face of cultural issues. Among the most memorably is the case of the exploding Ford Pintos.

Example 2: NiSource

A current example of cultural issues shaping a liability exposure involves NiSource, one of the nation’s largest natural gas distribution companies serving approximately 3.9 million customers in seven states.

Well aware of its reputation risk, which is disclosed in six mentions in the 2017 10K, it also acknowledges that angry disappointed stakeholders lead to “loss of cost recovery and increased litigation.” The board’s nominating and governance committee is charged with “reviewing and evaluating risks to the Company’s reputation and the steps management has taken to monitor and control such risks.”

After a series of gas explosions in the Boston area , and facing a complaint from the Governor of Massachusetts, the company undoubtedly faces costly liabilities and has already experienced a loss in market cap. However, they could in theory be much worse. In my firm’s experience, reputational value losses can exacerbate 3rd-party related liability losses by factors ranging from 2 to 7 times. What is helping to mitigate the reputational damage is that NiSource appears to have a genuine interest in the welfare of both its customers and employees, and such culturally-sensitive goodwill manifests in times like these where competing forces are battling for the mind of the stakeholder.

Reputation risk is the peril of stakeholders’ disappointment and anger when there is a gap between stakeholder expectations and reality. Noxious media typically amplifies that gap, which it certainly did in Facebook’s case.

Financial stakeholders may have been somewhat impressed with the company’s apparent sensitivity to reputation risk. Had they been more impressed, the company may have mitigated the loss in equity value which will trigger the inevitable pile on of litigators. How? Through the conventional practices of risk financing and transfer.

On a pro-forma basis, our firm modeled NiSource’s potential equity loss in a material crisis to be $764 million. Based on its inferred reputation risk management efforts, existing P/E ratios and other actuarial factors, a source of contingent capital from the pooled resources of an insurance captive and insurance markets of about $40 million would have materially dampened the stock market’s negative reaction.

Example 3: Weinstein and Company

Two other recent cases also illustrate weaknesses in the third pillar of a risk management framework: compliance-centricity.

In the matter of Weinstein and Company, the board was too close to the alleged perpetrator to be able to distance itself from the ethical breach. Stakeholders expect that, even with a strong CEO, a company’s board will be able to exercise appropriate oversight. As a result, found culpable in the court of public opinion, the firm was not salvageable.

Example 4: Wynn Resorts

On the other hand, at Wynn Resorts, the board successfully jettisoned the alleged perpetrator, Steve Wynn, protected itself from the opprobrium of gaming regulators and recovered all of its lost

The former Wynn Commons at the University of Pennsylvania. Photo by Natasha A. Kossovsky

equity value in under 20 weeks. The American Law Institute, in its upcoming publication  Principles of the Law, Compliance, Enforcement, and Risk Management for Corporations, Nonprofits, and Other Organizations,  is expected to address the timing discrepancy between courts of law and public opinion.

When it comes to mitigating enterprise-wide threats, reputation risk appears to be challenging existing risk management frameworks.

Risk managers must understand that the work involves mitigating not only negative media coverage but also anger and disappointment of stakeholders whose expectations have not been met.

In this mix, reputation insurances provide indemnifications that affirm trust and reduce economic losses.  &

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The views expressed in this article belong to the author and are not an editorial opinion of Risk & Insurance.

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Sponsored: Philadelphia Insurance Companies

How a carrier partner can help navigate a challenging management and professional liability market.

Rates in the management & professional liability (M&PL) markets were on the rise from 2020 to early 2023 and are now falling rapidly.

M&PL divisions manage a number of different insurance products including management liability (D&O), professional liability (E&O), employment practices liability (EPL), fiduciary liability policies, cyber, etc. In 2023 and into 2024, a big influence on the marketplace has been the extremely aggressive and softening public company D&O market.

Though these rates have been softening for management liability, that may change over the next few years as companies continue to adjust their business models motivated by economic uncertainty. Layoffs were up nearly 200% last year , Forbes reported, even as other recession indicators, like the inflation rate , improved. A recession could lead to an increased claim activity and force carriers to raise rates.

“Whenever there is a meaningful downturn in the economy, we tend to see claim frequency pop up,” said George Schalick, Jr., senior vice president of the Management and Professional Liability Division at Philadelphia Insurance Companies (PHLY).

With continued fiscal uncertainty, businesses potentially already burdened with pandemic-related claims should seek a carrier with a long history in M&PL products. They will provide much-needed risk management guidance and be better positioned to support their insureds during market fluctuations.

Why Insureds Might See an Uptick in M&PL Claims

George Schalick, Jr., Senior Vice President of the Management and Professional Liability Division, Philadelphia Insurance Companies

The current soft market might come as a bit of a surprise as it does not track with previous underwriting cycles and economic conditions. Afterall, many privately held and non-profit organizations struggled during the early days of the pandemic with shutdowns and rapidly declining revenues.  But the Government assistance programs, like the Paycheck Protection Program loans , helped keep many afloat during the tough times.

“During COVID many organizations stopped doing business until they were able to sort out all of the health and safety challenges,” Schalick said. “They were forced to lock down, but then all the government assistance programs allowed them to keep people employed. The increased volume of claims we anticipated we would see coming from the lockdowns and restrictions that were imposed upon businesses in the U.S. didn’t manifest at first.”

“Just because there wasn’t an onslaught of reported claims at the beginning of the pandemic, doesn’t mean the circumstances that would give rise to a claim being reported didn’t occur. Courts and the judicial system were closed or slowed and now that they are back open, we’re starting to see the circumstances that occurred during the COVID lockdowns becoming claims today,” Schalick said. “Litigation is progressing.”

Added to the delayed pandemic litigation is a concern over newer claims that might be filed as the country inches toward an economic downturn. Though a recession was avoided in 2023, experts think a soft dip could occur in 2024, with 76% of economists saying there’s a 50% or less chance of an economic downturn this year — that almost always results in more management liability claims.

“During the Great Recession in 2008, we saw an almost immediate spike in claims because of the economic conditions and the pressure it placed on organizations. They were making personnel changes with significant belt tightening almost immediately.” Schalick said.

What’s in Store for M&PL Policy Rates in 2024?

Despite an uptick in claims and increased economic uncertainty, management liability rates haven’t increased, resulting in market-wide pricing levels that may not meet the increased pressure of rising settlements and jury verdicts.

“Rates are going the other direction and settlement values are not falling,” Schalick said.

The mismatch between rates, claim frequency and severity is, in part, because carriers experiencing the dramatic soft market in the public D&O market are seeking premium gain in the private and non-profit market.

“In the public company market, the rates have been decreasing significantly. The rates were increasing in the private, not-for-profit market, and rightfully so, but there’s a desire to supplement overall mid-size D&O for carriers who also write private not-for-profit, and they see that as an opportunity to aggregate premium,” Schalick said. “So the always competitive landscape in the private, not-for-profit market has dramatically increased in the last 18 to 24 months.”

Still, companies of all sizes and types should be concerned about management liability rates in the future. Legal system abuse is resulting in increases in both the amount of litigation and the size of verdicts plaintiffs are receiving.

Certain areas of the country are particularly vulnerable to this type of legal system abuse. As a result, insureds in these localities are likely to be vulnerable to rate increases.

“The environment is so positive for the plaintiff that forces premium increases so carriers are able to stay in that market long term,” Schalick said.

Why a Tenured Carrier Partner Can Help Insureds Navigate An Uncertain Market

It’s clear that insureds are facing an uncertain M&PL market over the next few years. Fortunately, carriers with a long history in the M&PL space will be there to offer stability.

Philadelphia Insurance Companies has been supporting this market for 35 years. PHLY is committed to offering long-term rate stability, even as economic and claims trends start to push premiums upwards. They have an appetite for all sorts of companies, large and small, for-profit and nonprofit alike.

“We’ve been at this game for a long time and are one of the most tenured underwriters in this space,” Schalick said. “We like to stay very consistent.”

  PHLY has worked with both for-profit and non-profit on management liability policies. With dedicated M&PL teams throughout the company’s 13 regions, PHLY provides the support agents and brokers are looking for on behalf of their clients. The teams know their regions well and can respond to local trends. They’re also dedicated to making the renewal process as easy as possible for their partners and policyholders.

“We have real confidence in our results, so we focus a lot on making the renewal experience as painless as possible for all agents and insureds,” Schalick said.

The company is also investing in tools to help insureds avoid losses. Earlier this year, they launched a new online risk management platform, PHLYGateway, which offers resources for insureds on how to create an employee handbook and trainings on issues such as recognizing workplace sexual harassment and discrimination.

If insureds have questions, they can consult a Best Practices Help Line, provided via the platform. That way, they can get on the spot risk management guidance to help them prevent claims.

To learn more, visit: https://www.phly.com/mplDivision/managementLiability/default.aspx .

This article was produced by the R&I Brand Studio, a unit of the advertising department of Risk & Insurance, in collaboration with Philadelphia Insurance Companies. The editorial staff of Risk & Insurance had no role in its preparation.

Risk Management and Insurance Case Study

Introduction.

Risk management refers to the concept of identifying, assessing, evaluating, prioritizing, of possible risks that a firm or an individual faces in a bid to minimize, control, or monitor impact of identified risks through applications of resources. One of the ways of controlling or minimizing impact of risks is the risk transfer (Dorfman, 2007).

Risk transfer, also known as insurance, involves engagement of a third party through a contract to pay a given sum of money in the event that such a suspected loss occurs. Insurance contracts involve premium and principles of insurance.

One of the principles is subrogation and indemnity requiring insurer to pay insured sum assured in the event that a loss is caused by insured risks.

The following scenarios confirm how the principle of indemnity and contribution affects insurance practices.

You have purchased a homeowner’s insurance policy for your home that you live in with your spouse and 2 children of 19 and 17. You live in a single family residence built in 1996 that is 1 story with 3 bedrooms and 2 ½ bathrooms. The coverages for your policy are as follows:

Coverage A: $190,000

Coverage B: $19,000

Coverage C: $75,000

AOP Deductible: $1,000

Coverage D: $38,000

Coverage E: $300,000

Coverage F: $5,000

Hurricane Deductible: 2%

You also purchase for your insurance an auto policy covering all 4 drivers in your household and the 3 vehicles you own. The coverage in your auto policy is as follows:

• Personal Injury Protection: $10,000 ded: $0
• Liability: Bodily Injury $50,000 / $100,000
• Liability: Property Damage $50,000
• Uninsured Motorist: $50,000 / $100,000
• Medical Payments: $5,000
• Collision Deductible: $500
• Comprehensive Deductible: $500

Both policies were purchased on March 1st, 2012 and are for 1 year. During the year your household had the following claims. Please indicate how much the insurance company is required to pay for the claims and under which coverage are they paying:

• April 12th,2012: a water pipe burst in your kitchen while the dinner was being cooked and it produced $69,000 to your home and $5,500 to some small appliances and kitchen items.Water pipe is part of the constructed house hence any losses associated with physical damages caused to any part of the property is compensated on the basis of coverage A (Dorfman, 2007). Therefore, the amount of $74,500 will be compensated from the $190,000 Coverage A taken by the policy holder.
• May 21st, 2012: you son driving back from school while raining loses control of the vehicle and hits a traffic signal knocking it down. The city sues you to repair the damage and is awarded by the court a judgment for $83,525. Your son did not suffer any injuries but the vehicle required $8,600 in repairs. The insurance will pay a sum of $50,000, which was the principal sum insured for property damages under the auto policy. The owner will have to meet the cost of the remainder, which is $89,525 – $50,000 = 39,525. This is because the insurance firm only promised to indemnify the policy holder up to $50,000 in case of any property damages under the auto policy. However, the owner will not have to pay the remainder as the insurance policy will under Coverage E (Vaughan & Vaughan, 2007).
• July 16th, 2012: Hurricane Jimmy barreled through South Florida and caused wind damage to your home in the amount of $105,000 in repairs and $91,500 to your personal property inside. The total damage of the hurricane is $204,500. Given the hurricane deductible of 2%, the insurance will pay the difference between damages caused and the deductible derived from the sum assured (Dorfman, 2007). The deductible is 2% of 672,000 = $12,450. Therefore, the insurance firm will pay $192,050 ($204,500 – $12,450) based on Coverage E.
• August 20th, 2012: After several days of constant very heavy rains in the afternoon in South Florida, waters level went up and caused extensive flooding in your neighborhood. The rise of these flood waters caused $14,500 of damage to your home, $28,000 to your personal property, and $6,000 to your automobile. Total damages caused by the flood were $48,500. Coverage C takes care of all personal property loss caused by water losses, fires, floods, hurricanes, and any other causes that lead to damage of personal property (Harrington & Niehaus, 2003). Insurance firm will pay the $48,500 from the Coverage C policy.
• February 14th, 2012: while cooking a Valentine’s Dinner for spouse and the kids were away at a friend’s house your kitchen caught on fire but this time it caused a major short circuit that caused the flames to grow quickly and the house totally burned down with all your belongings being destroyed. The fire also spread to two neighbors properties who then successfully sued you in court for their losses: the first had damage to their home for the amount of $109,000 and belongs for $98,000; the second for damage of $174,000 for their home, $103,000 for belongs, and $58,000 for their car that was completely destroyed in the garage. It was necessary to spend $61,000 to rent another place while your home was being rebuilt. The total damages will be paid by the insurance policy given that all the possible coverages and auto policies were taken enough to play a role in compensating the insured for the loss of the house. All the coverages taken will come into play to provide the compensation since the house was brought down by fire.
• March 10th, 2013: Your son had a car accident where he hit another car and overturned your vehicle for a total loss. Your son fortunately was not hurt in the accident because of his seatbelt but your car had a total loss valued at $31,000. The other car he hit had two passengers who suffered extensive injuries: the driver required surgery and hospitalization for $101,500 and the passenger was in coma for 2 months and required surgery costing $233,000 in medical bills. The other car was also a total loss and was valued at $43,500.

Under the following, the insurance will provide compensations for the losses incurred during the accident. Liability policy that was taken in the amount of Property Damage $50,000 will be used to compensate for the $31,000 loss of the car.

Under the Bodily Injury liability policy of $50,000 / $100,000, the insurer will compensate for the loss caused to the other parties. Since the insured had a comprehensive policy with a deductible of $500, the insurer will pay all the losses caused to the third party less $500.

Dorfman, M. (2007). Introduction to risk management and insurance (9 th ed.). Upper Saddle River, NJ: Prentice Hall.

Harrington, S. & Niehaus, G. (2003). Risk management and insurance. New York, NY: McGraw-Hill.

Vaughan, E. & Vaughan, T. (2007). Fundamentals of risk and insurance. New York, NY: John Wiley & Sons.

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IvyPanda. (2019, April 17). Risk Management and Insurance. https://ivypanda.com/essays/risk-management-and-insurance/

"Risk Management and Insurance." IvyPanda , 17 Apr. 2019, ivypanda.com/essays/risk-management-and-insurance/.

IvyPanda . (2019) 'Risk Management and Insurance'. 17 April.

IvyPanda . 2019. "Risk Management and Insurance." April 17, 2019. https://ivypanda.com/essays/risk-management-and-insurance/.

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In this case study, an accident caused by a customer resulted in serious employee injuries and significant property damage.

At about 6:30 p.m. on Wednesday, July 23, 2014, a patron was leaving a pub in southeastern Wisconsin. Intending to pull straight out of his parking stall, he accidentally put his vehicle into reverse and accelerated, backing into the building and caving in the wall. Meanwhile, inside the pub, an employee was serving drinks from behind the bar, which is near a cooking area with a broaster. Suddenly, scalding hot grease erupted from the broaster, splashing everything nearby. The vehicle had hit the wall that contained the cooking equipment, causing serious injuries to the pub employee and significant damage to the building.

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A case study in risk management (Risk and insurance series) Paperback – January 1, 1972

• Print length 160 pages
• Language English
• Publisher Meredith Corp
• Publication date January 1, 1972
• ISBN-10 0390760102
• ISBN-13 978-0390760104
• See all details

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• Publisher ‏ : ‎ Meredith Corp (January 1, 1972)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 160 pages
• ISBN-10 ‏ : ‎ 0390760102
• ISBN-13 ‏ : ‎ 978-0390760104
• Item Weight ‏ : ‎ 12.8 ounces
• #2,574 in Risk Management (Books)

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• Case Studies

General Electric's Financial Collapse: Risk Management Case Study

written by Thomas Johnson , On September 08, 2023

General Electric is a multinational corporation globally recognized for manufacturing and fabricating home appliances, technologies, aviation, engines, power generation, gas, etc. Their broad portfolio also includes equity investment, and for a company that has it all and with over 131 years of founding, they have the experience and resources to manage financial risk correctly. 

However, by 2018, the scandal shocked shareholders and investors of this multinational, with a steep drop in share value of more than 70%. 

Today, we explain the General Electric risk management case study, what the risk management teams did not see, what events generated the fall, the consequences they faced, and how financial losses could have been avoided. 

Let's get started!

What does General Electric Company do?

General Electric is an American company founded in April 1892 by Thomas Alva Edison, J.P. Morgan, Charles Coffin, Edwin Houston, and Elihu Thomson, originally dedicated to the electrical sector. As its slogan said, " We bring good things to life ." The company changed people's lifestyles, and in most American homes and around the world, you could find items created by this company, from light bulbs, lamps, refrigerators, toasters, microwaves, and many others. 

Over time, GE diversified its portfolio by acquiring multiple patents , and today, it is a multinational conglomerate of technological infrastructure and numerous financial services with a presence in more than 100 countries. General Electric offers various products and services, including electrical distribution, home appliances, electric motors, gas, locomotives, software, petroleum, aviation, and insurance.

This ability to cover multiple industries led it to position itself as the fifth-largest company in the world and the 14th most profitable in 2011 . This context allows us to understand why acquiring GE company shares attracted stock market investors. Still, they should have counted on the fact that there were flaws in the profitability figures they received. 

Let's see what went wrong!

General Electric scandal: Accountant mismanagement

By 2018, the Securities and Exchange Commission surprised investors by announcing that GE's share price had fallen by 76% of its value due to the deterioration of its energy and insurance businesses.  

To understand how this multinational reached this critical point, let's look at the events and risks they failed to manage, ultimately generating the decline in this risk management case study.

Insurance business decline

For 2018, GE's insurance business reported severe financial losses of $6.2 billion. This division provided insurance to nursing homes and assisted living facilities. However, rising healthcare costs and extended life expectancy resulted in substantial losses for the business. 

Reduced cost estimates

In 2017, General Electric presented investors with earnings estimates for 2015 and the first two quarters of 2017, which projected a substantial increase in annual revenue. However, the company omitted critical drivers of that purported increase in profitability, which stemmed not from increased demand for insurance policies but from a substantial reduction in projected costs .

Hiding of insider sales

GE and its management should have informed investors about a significant acquisition of the company, which inflated its value. The company conducted an internal sale of receivables between GE Power and GE capital, so the figures reflected future years' cash.

Lack of transparency

When companies list their shares on the stock exchange, they commit to providing truthful and accurate information about their operations and the results each of them has; this ensures the reliability of the values at which their shares are set. However, in the case of GE, the accounting team deliberately presented information about expected growth, which motivated investors to buy. In addition, it concealed rising claims costs from policyholders and the injection of funds of an undeclared nature.

Repeated Failures and Violation of Anti-Fraud Policies

GE's conduct was directly contrary to disclosure policies and laws, accounting controls, and those provided by securities law. Continued failures to disclose information about GE's energy and insurance financial status, including failure to disclose the nature of the $2.5 billion in cash from the energy business. 

Find out what GE had to deal with when it all came to light!

Consequences of Poor Financial Risk Management

A 200 million fine..

After a lengthy investigation for more than three years by the Security and Exchange Commission (SEC), the regulatory agency ordered GE company to pay a fine of 200 million dollars and to dismantle its empire to pay the amount owed . 

Note:  Although it promised to pay the fine, GE never admitted responsibility for the accounting reports. 

A company without a leader.

At the time of the General Electric scandal, the company was headed by Jeff Immelt, who, after more than 16 years, had to resign from his position and was replaced by John Flannery. However, after only one year at the head of the company, Flannery was dismissed, and Larry Culp arrived, who had to deal with the consequences of the disaster. 

Financial losses that meant the end

The insurance division finally had to write off 9.5 billion dollars in taxes and dismantle the insurance business. In addition, GE company shareholders had to inject an estimated $15 billion in capital to deal with the consequences . 

How could poor financial risk management have been prevented?

Pirani: Track your risk and improve regulatory compliance.

Pirani is a risk management software that allows companies to control potential threats; with an easy-to-use and managed interface, the tool helps to optimize the identification and analysis of risks. Once potential risks have been detected, you can create risk matrices to prioritize those most likely to occur, i.e., The increased medical supplies. In addition, the software presents heat map views to prioritize risks according to their severity, which helps to focus efforts and resources.

Pirani allows direct communication across all areas and levels, as it centralizes all essential information accessible to all members. It is also a flexible option configured according to the regulations applicable to each organization to facilitate regulatory compliance. It also allows timely monitoring of the risk control measures implemented and the progress of action plans. 

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• Open access
• Published: 23 April 2024

Enhancing pooling levels strengthens the risk resilience of healthcare insurance: a case study of basic medical insurance fund operations data in Gansu, China

• Feng Hu 1 ,
• Liu Heming 1 ,
• Cao Wenxuan 1 ,
• Wang Xuemei 1 ,
• Liang Qijun 2 &
• Hu Xiaobin 1  

BMC Public Health volume  24 , Article number:  1129 ( 2024 ) Cite this article

Metrics details

In China, enhancing the pooling levels of basic health insurance has consistently been regarded as a pivotal measure to promote the refinement of the healthcare insurance system. From 2020 to 2022, the widespread outbreak of COVID-19 posed new challenges to China’s basic health insurance.

The research utilizes Data Envelopment Analysis (DEA), Malmquist index assessment, and fixed-effects panel Tobit models to analyze panel data from 2020 to 2022, assessing the efficiency of basic health insurance in Gansu Province.

From 2020 to 2022, the average overall efficiency of the municipal pooling of Basic Medical Insurance for Urban and Rural Residents was 0.941, demonstrating a stable trend with a modest increase. The efficiency frontier regions have expanded from 5 (35.71%) to 7 (50%). Operational efficiency exhibited a negative correlation with per capita hospitalization expenses and per capita fund balance but a positive correlation with per capita accumulated fund balance and reimbursement rates for hospitalized patients. In 2021, compared to 2020, the county-pooling Basic Medical Insurance for Urban Employees saw a decline of 0.126 in overall efficiency, reducing the efficiency frontier regions from 8 to 3. However, from 2021 to 2022, the municipal-coordinated Basic Medical Insurance for Urban Employees experienced a 0.069 increase in overall efficiency, with the efficiency frontier regions expanding from 3 to 5. Throughout 2020 to 2022, the operational efficiency of the Urban Employee Basic Medical Insurance showed a consistent negative correlation with per capita fund balance.

From 2020 to 2022, the overall operational performance of basic health insurance in Gansu Province was satisfactory, and enhancing the pooling level is beneficial in addressing the impact of unforeseen events on the health insurance system.

Peer Review reports

Introduction

Health holds paramount importance on a global scale [ 1 ]. The inception of a robust medical insurance system holds immense significance in preserving public health, promoting health awareness, optimizing the allocation of medical resources, and sustaining social progress [ 2 ]. The basic medical insurance system reflects the crucial emphasis of the state and society on the health and welfare of the populace. It is essential for promoting the overall health of the population and public health [ 3 , 4 ]. China’s social medical insurance system has undergone significant evolution since the establishment of urban employees’ basic medical insurance (UEBMI) in 1998 and the subsequent introduction of the new rural cooperative medical care system in 2003 [ 5 ]. The completion of nationwide coverage occurred in 2009 with the establishment of urban resident basic medical insurance [ 6 ]. In 2016, China’s State Council issued opinions on integrating urban and rural basic medical insurance systems, merging urban residents’ basic medical insurance and new rural cooperative medical care into a unified system to enhance operational efficiency.

However, in the ongoing process of enhancing basic medical insurance, the challenge of the pooling level, commonly referred to as “vertical fragmentation,” persists and requires further attention [ 7 , 8 ]. The term “vertical fragmentation” within the healthcare insurance system denotes the presence of independent policies and operational regulations across various administrative levels, including provinces, cities, and counties. This results in a fragmented state within the entire healthcare insurance system. In China’s basic medical insurance system, this phenomenon is notably conspicuous, primarily manifesting through institutional fragmentation, unequal benefits, and a lack of coordination in reform initiatives. Consequently, basic medical insurance at lower pooling levels is suggested to have a constrained ability to manage risks during unforeseen public events [ 6 , 9 ]. Upgrading the level of pooling is considered to be the main means of increasing the operational efficiency of health insurance and improving its risk resistance.

Municipal pooling of basic medical insurance has been extensively implemented across China [ 10 ]. In response to the challenge of vertical fragmentation, Gansu Province, in 2019, elevating the pooling of URRBMI to the municipal level, guided by the Gansu Province Municipal Pooling of Urban and Rural Residents’ Basic Health Insurance Implementation Opinions policy. And, in 2021, the Gansu Provincial Health Insurance Bureau and the Department of Finance issued a Circular on Further Implementing Municipal Pooling of Urban Employees’ Basic Medical Insurance. This circular stipulated that all municipalities in Gansu Province were to achieve municipal pooling of UEBMI by January 1, 2022.

Literature review

Elevating the standard of fundamental health insurance pooling is widely recognized as pivotal for addressing “vertical fragmentation,” enhancing operational efficiency within the health insurance system, and bolstering its risk tolerance. Smith P. C.‘s examination of diverse risk pooling models highlights the detrimental effects of coordination deficiencies on the health system, advocating for heightened pooling levels [ 11 ]. Similarly, Ali Ahangar argues for increased pooling levels in health insurance, citing the scale and uncertainty of individual medical expenditures, which, when addressed, can reduce uncertainty and facilitate effective risk-sharing [ 12 ]. Naoki Ikegami and peers qualitatively analyze Japan’s universal health insurance evolution, underscoring the necessity of elevated pooling levels for long-term sustainability and equity [ 13 ]. Shibuya et al. identify threats to Japan’s universal health insurance sustainability and propose elevating pooling levels as a safeguard [ 14 ]. Additionally, McIntyre et al.‘s retrospective study on South Africa’s health insurance development emphasizes the importance of establishing an integrated fund pool to rectify resource disparities between public and private sectors [ 15 ].

Research on enhancing the pooling level of basic medical insurance in China encompasses empirical, theoretical, necessity, and factor analysis studies. Luo Jiaying construct a provincial-level model for UEBMI in Fujian Province, utilizing hierarchical analysis with data on insurance participation across coordination areas, advocating for its feasibility [ 16 ]. Fu Mingwei. address the transition from municipal to provincial-level pooling, employing a Probit model for empirical analysis, marking a significant empirical inquiry into provincial pooling [ 17 ]. Some scholars offer qualitative insights on elevating China’s basic medical insurance pooling level [ 18 , 19 ]. Regarding influencing factors, Li Yaqing identifies moral hazard escalation as a risk factor post-coordination level increase [ 20 ]. Fu Mingwei, utilizing a Probit model, identify urban workers’ insurance participation and the proportion of financially governed counties and districts as pivotal factors influencing provincial-level coordination advancement [ 17 ]. Qingyue Meng, synthesizing domestic and international studies on insurance integration, assert its significance in reducing inter-scheme disparities, enhancing risk-sharing, service coverage, financial protection, operational efficiency, and health system integration [ 6 ]. They stress the broader service and protection for rural residents, the elderly, and the chronically ill, along with addressing challenges posed by population mobility [ 6 ].

In the realm of health insurance pooling elevation, research has predominantly focused on delineating its benefits, imperative, strategies, and influencing factors. However, extant studies regarding how augmenting basic health insurance levels can bolster risk resilience primarily lean on the “law of large numbers” as a theoretical foundation. Hence, this study delves into pertinent research on advancing health insurance coordination through the following avenues: (i) Utilizing operational data from Gansu Province’s basic health insurance fund spanning 2020–2022, we employ the DEA model to assess the efficiency of UEBMI alongside URRBMI. (ii) Considering the disparate municipal pooling attainment timelines for the two basic health insurance types in Gansu Province, China, we analyze the COVID-19 pandemic’s impact on system operational efficiency across varied pooling levels, comparing the URRBMI with the UEBMI and assessing enhancement pooling efficiency scores. (iii) Employing the Malmquist index and panel data Tobit model, we comprehensively scrutinize basic health insurance operational efficiency across different periods, probing its influential factors. Ultimately, our study furnishes empirical evidence supporting the notion that elevating basic medical insurance pooling levels can enhance fund operational efficiency and fortify its resilience against risks, thereby furnishing a groundwork for policy formulation geared toward pooling enhancement in medical insurance.

To facilitate reader comprehension, a graphical representation illustrating the research framework has been devised (Fig.  1 ).

Research framework

Methodology

Data sources.

The data employed in this study comprises 14 variables, covering 14 cities in Gansu Province from 2020 to 2022. These variables constitute panel data. Specifically, the Fund Operation Report of the Gansu Provincial Bureau of Medical Security provided data on fund income (in RMB 100 million), fund expenditure (in RMB 100 million), the number of insured individuals, fund balance (in RMB 100 million), cumulative fund balance (in RMB 100 million), hospitalization rate (%), and the actual reimbursement ratio of hospitalized patients (%) for both URRBMI and UEBMI. Furthermore, data on the number of health technicians per 10,000 people for the years 2020–2021, the average salary of the urban population, GDP per capita, and year-end population figures were obtained from the Gansu Provincial Statistical Yearbook (2021–2022) [ 21 ]. For 2022, data from the Gansu Provincial Bureau of Statistics Statistical Bulletin of National Economic and Social Development of Cities and Prefectures (2022) [ 22 ]. The Gansu Provincial Health and Wellness Statistical Yearbook (2021–2023) provided data on per capita outpatient expenses (in RMB), per capita inpatient expenses (in RMB), the number of medical institutions, and the number of tertiary hospitals.

Selection of indicators

Selection of appropriate input and output indicators is a crucial prerequisite for using the DEA model to assess the operational efficiency of URRBMI and UEBMI. In establishing the evaluation framework, this study has summarized existing research on the use of the DEA model to assess social insurance efficiency. Notably, in the context of China, studies related to the operational efficiency of social insurance commonly employ fund input, the number of healthcare personnel, and the number of insured individuals as input indicators, while fund expenditure and indicators reflecting patient hospitalization characteristics are used as output indicators (Table  1 ).

Input variables refer to the resources or factors utilized in the production process, representing the critical resources consumed by decision units in the production. On the other hand, output variables signify the outcomes or products generated by decision units through the utilization of these input variables. In developing the indicator framework, this study considered the principles of representativeness, objectivity, and feasibility. Combining these principles with expert opinions, the study ultimately determined the input indicators for URRBMI to be: fund income, the number of healthcare personnel per 10,000 people, and the number of insured individuals. For UEBMI, the input indicators include: fund income, the number of healthcare personnel per 10,000 people, the number of insured individuals, and the average wage of urban employees. The output indicators for both types of basic medical insurance were determined to be fund expenditure and hospitalization rate. Additionally, factors such as per capita inpatient costs, per capita outpatient costs, per capita fund balance, per capita cumulative fund balance, the actual reimbursement ratio for inpatients, per capita GDP, the number of medical institutions per 10,000 people, and the proportion of tertiary-level medical institutions were considered as variables influencing the comprehensive technical efficiency of the fund. Table  2 provides a detailed explanation of the indicators.

Statistical test

Data envelopment analysis.

Data Envelopment Analysis (DEA) was a widely used non-parametric technique for determining each decision-making units (DMUs) relative efficiency score and evaluating the linkages between inputs and outputs within different DMUs [ 27 ]. A linear programming model was employed to determine the weights assigned to each DMU, either minimizing inputs or maximizing yield, to gauge the relative efficiency levels concerning resource utilization and output. An advantage of DEA was its ability to manage the complexities associated with multiple inputs and outputs. By comparing the relative efficiency scores of DMUs, one could identify the most efficient DMU, with a score of 1 denoting optimal efficiency. The input-oriented BCC model (Variable Returns to Scale) was used in this study to evaluate efficiency. The linear form of the BCC model is as follows

Malmquist index

The Malmquist index was a significant indicator used to measure changes in technical efficiency between two periods (usually involving two points in time) [ 28 ]. Its calculation relies on the DEA principle, where the Total Factor Productivity Efficiency (TFPCH) index was determined using a distance function. Efficiency Change (EFFCH) and Technical Change (TECHCH) are the two components of the Malmquist index, respectively, and Pure Efficiency Change (PHCH) and Scale Efficiency Change (SECH) are the two further components of EFFCH. The formula appears as follows:

M 0 represented the Total Factor Productivity Efficiency (TFPCH) index for the period (m + 1) relative to the period (m). Assuming the variable returns to scale, if M 0 was more than 1, it indicates an improvement in production efficiency for that period; if M 0 was less than 1, it signified a decrease in production efficiency.

Tobit model

Since the operational efficiency of URRBMI and URBMI fell within the range of 0 to 1, categorizing them as bounded dependent variables, this study employed the Tobit model to investigate the factors that influenced the efficiency of basic medical insurance operations in Gansu Province. The Tobit model, initially proposed by James Tobin, was widely utilized for handling truncated data [ 29 ]. Both the fixed effects panel data Tobit model and the random effects panel data Tobit model were simultaneously utilized in this study. The Stata program developed by Honor, Bo E. (1992) was employed for fixed effects panel data Tobit model fitting [ 30 ]. The Hausman test was used to choose between the panel data Tobit fixed effects model or the random effects model. Model fitting was conducted using Stata 15.0 software, with a significance level set at α = 0.05.

Current status of the operation of the basic medical insurance

This study analyzed the operation of URRBMI and UEBMI in Gansu Province through non-parametric tests. Table  3 revealed significant differences between these two types in several aspects. Specifically, these differences were observed in fund income ( Z = -2.89, P  = 0.004), the number of insured individuals ( Z = -6.566, P  = 0.000), hospitalization rate ( Z = -3.525, P  = 0.000), fund expenditure ( Z = -3.306, P  = 0.001), cumulative fund balance ( Z = -2.774, P  = 0.006), and the actual reimbursement ratio for hospitalized patients ( Z = -7.694, P  = 0.000).

DEA modeling results

As indicated in Table  4 , from 2020 to 2022, the average TE of URRBMI operation in Gansu Province was 0.941, with an average PTE of 0.955 and SE of 0.985. In 2022, the TE was 0.957, showing a generally stable and slightly increasing trend, with 7 out of 14 (50%) DMUs operating on the efficiency frontier. Meanwhile, for UEBMI operation during the same period, the average TE was 0.900, with an average PTE of 0.923 and an average SE of 0.974. The overall trend exhibited an initial decrease followed by an increase. In 2022, the TE was 0.904, with 35.71% of the regions operating on the efficiency frontier.

Results of the Malmquist index model

Malmquist index-urrbmi.

Figure  2 illustrates the regional distribution of the TFPCH index for URRBMI between 2020 and 2022. Over the study period, TFPCH indexes greater than 1.000 were observed in 6 cities (42.86%), indicating an increasing trend in the operational efficiency of URRBMI in these areas. Conversely, eight municipalities and prefectures (57.14%) had TFPCH indexes of less than 1.000, suggesting a declining trend in URRBMI’s operational efficiency in those regions. It is noteworthy that Jiuquan City (8), Zhangye City (6), and Pingliang City (7) had relatively higher TFPCH values, while Linxia Hui Autonomous Prefecture (12), Tianshui City (4), and Longnan City (11) exhibited relatively lower TFPCH values.

The variation in the total factor productivity changes (TFPCH) of the basic medical insurance for urban-rural residents in 14 municipalities during the period from 2020 to 2022

Table  5 presents the Malmquist indices for the operation of URRBMI in each city and prefecture. The TFPCH index for URRBMI from 2020 to 2021 was 1.036, with an EFFCH index of 0.998 and a TECHCH index of 1.039. From 2021 to 2022, the TFPCH index was 0.884, with an EFFCH index of 1.010 and a TECHCH index of 0.875. Over the period from 2020 to 2022, the average TFPCH was 0.957, indicating an overall declining trend in production efficiency. During the study period, the TECHCH was 0.953, contributing to the TFPCH being less than 1.000.

Malmquist index-UEBMI

Figure  3 shows the regional distribution of TFPCH of UEBMI operation from 2020 to 2022. During this period, seven municipalities and prefectures (50.00%) had TFPCH indices of more than 1.000, indicating an increasing trend in the operational efficiency of UEBMI in these areas. Conversely, seven other municipalities and prefectures (50.00% of the total) had TFPCH indices of less than 1.000, suggesting a declining trend in UEBMI’s operational efficiency in those regions. It is noteworthy that Jiuquan City (8) and Pingliang City (7) had relatively higher TFPCH indices, while Jinchang City (2) had the relatively lowest TFPCH index.

The variation in the total factor productivity changes of the urban employees’ basic medical insurance funds for in 14 municipalities during the period from 2020 to 2022

Table  6 displays the Malmquist indices for UEBMI operation in various cities and prefectures. The TFPCH index from 2020 to 2021 was 1.035, exceeding 1.000, indicating an increase in the production efficiency of UEBMI operations in Gansu Province during this period. However, from 2021 to 2022, the TFPCH index was 0.957, below 1.000, suggesting a decrease in the production efficiency of UEBMI operations in Gansu Province during this period. When considering the data from 2020 to 2022, the TFPCH index was 0.995, also below 1.000, indicating a declining trend in the overall production efficiency of UEBMI operation in Gansu Province. The decrease in UEBMI’s TFPCH index owed to a reduction in the EFFCH index.

Panel Tobit model regression results

This study utilized the TE scores from the DEA models for the operation of basic medical insurance in various cities and prefectures from 2020 to 2022 as the dependent variable. Two separate models, the random effects panel data Tobit model and the fixed effects panel data Tobit model, were fitted, and the model selection using the Hausman Test. Table  7 indicated that the results of the random effects panel data Tobit model and the fixed effects panel data Tobit model were relatively consistent for the operational efficiency of the URRBMI. The Hausman Test results demonstrated that the fixed effects panel data Tobit model outperformed the random effects panel data Tobit model ( χ 2 = -2.32). However, for the operational efficiency of the UEBMI, there were significant differences between the results of the random effects panel data Tobit model and the fixed effects panel data Tobit model. The Hausman Test results revealed that the fixed effects panel data Tobit model was superior to the random effects panel data Tobit model ( χ 2 = -10.02).

Table  8 presents the results of the fixed effects Tobit regression model for the efficiency of URRBMI operation. The results indicate that the lower the per capita hospitalization cost, the higher the operational efficiency ( β = -0.000052, 95% CI : -0.000099 ∼ -0.000004, P  = 0.033); the lower the per capita fund balance, the higher the operational efficiency ( β = -0.000116, 95% CI : -0.000180 ∼ -0.000051, P  = 0.000); the more per capita cumulative fund balance, the higher the operational efficiency ( β  = 0.000036, 95% CI : 0.000002  ∼  0.000071, P  = 0.041); and the higher the actual reimbursement ratio for hospitalized patients, the higher the operational efficiency ( β  = 0.005960, 95% CI : 0.000494  ∼  0.011427, P  = 0.033).

Table  9 presents the results of the fixed effects Tobit regression model for the efficiency of UEBMI operation. The research findings indicate that the lower the per capita fund balance, the higher the operational efficiency ( β = -0.0000787, 95% CI : -0.0001181 ∼ -0.0000392, P  = 0.000); and the lower the medical institution density, the higher the operational efficiency ( β = -0.0031376, 95% CI : -0.0049025 ∼ -0.0013726, P  = 0.000).

This study employed the DEA-Malmquist-Tobit model to assess the operational efficiency of basic medical insurance in the Gansu region of China and conducted an in-depth exploration of its influencing factors. The results revealed that the average TE score for URRBMI was 0.941, showing a generally stable trend with slight improvement, while UEBMI had an average TE score of 0.900 with noticeable fluctuations. From 2020 to 2022, the TFPCH for URRBMI was 0.957. The decrease in TECHCH explained the decline in overall production efficiency during 2021–2022. For UEBMI, the TFPCH was 0.995, with EFFCH being less than 1.000, serving as a primary reason for TFPCH being below 1.000. The study found that a rise in per capita hospitalization expenses and per capita fund balance negatively affected the operational efficiency of URRBMI. Conversely, an increase in per capita cumulative fund balance and the actual reimbursement ratio had a positive impact. For UEBMI, its operational efficiency decreased with an increase in per capita fund balance and medical institution density.

From 2020 to 2022, the average TE of URRBMI in Gansu Province was 0.941, while that of UEBMI was 0.900. China’s URRBMI from 2017 to 2020 was estimated to have a TE of 0.921 compared to other research using comparable methodologies [ 23 ]. Some research has characterized Gansu Province’s URRBMI as a “low-input, high-efficiency” fund operation model [ 32 ]. The average TE of China’s UEBMI from 2017 to 2019 was 0.817 [ 33 ]. Additionally, studies have affirmed that regions with lower economic levels can more effectively utilize healthcare resources [ 34 , 35 , 36 ]. Throughout the study period, URRBMI outperformed UEBMI in terms of both average TE and stability. The outbreak of COVID-19 at the end of 2019 posed significant threats to global economic development, social stability, and human health, particularly challenging healthcare systems. Gansu Province experienced two waves of pandemic peaks in 2021 and 2022. In Gansu Province, URRBMI had implemented city-level pooling earlier than UEBMI. Relevant studies have reported that enhancing the pooling level of healthcare insurance can improve its operational efficiency and risk resilience [ 11 , 37 ]. That could be one of the reasons why the average level and stability of URRBMI’s operational efficiency during the pandemic period were superior to those of UEBMI.

The results of the Malmquist index analysis indicate that the average TFPCH index for both URRBMI and UEBMI from 2021 to 2022 was below 1.000, suggesting an overall decline in the efficiency of healthcare resource utilization within the basic medical insurance systems during this period. In the case of URRBMI, the TFPCH below 1.000 was driven by TECHCH. On one hand, due to the COVID-19 pandemic, a significant portion of healthcare resources was allocated to managing the outbreak and researching COVID-19 treatments [ 38 ], resulting in a temporary reduction in the supply of certain healthcare services. On the other hand, to mitigate the risk of infection, some patients postponed or avoided non-urgent medical assistance, leading to a temporary decrease in the demand for healthcare services [ 39 , 40 ]. While this enhanced financial stability for the fund management agencies of URRBMI, it may have translated to reduced accessibility to healthcare services for insured individuals. However, for UEBMI, the TFPCH below 1.000 was attributed to EFFCH. Suggests that UEBMI may face multifaceted challenges. Firstly, the healthcare system experienced significant stress due to the impact of COVID-19 [ 38 ]. Secondly, in 2022, Gansu Province’s UEBMI had just achieved municipal-level pooling, and the department responsible for the fund might not yet be familiar with the policies and management methods. Indicates that the fund management agencies for UEBMI need to address issues related to inadequate resource utilization, improvements in fund operation strategies, and sustainability. For insured individuals, these challenges may impact the quality of services and hinder the satisfaction of healthcare needs.

Per capita hospitalization expenses show a negative correlation with the operational efficiency of URRBMI. First off, as per capita hospitalization costs increase, the health insurance fund is put under more financial strain, which could result in diminished solvency or even financial difficulties. Second, the irrational distribution of healthcare resources among districts may be exacerbated as costs increase, thus reducing the efficiency of the fund and affecting the provision of other healthcare services [ 41 ].

Per capita fund surplus exhibits a negative correlation with the operational efficiency of URRBMI and UEBMI, whereas per capita accumulated fund surplus shows a positive correlation with URRBMI. The outbreak and widespread prevalence of COVID-19 at the end of 2019 led to a decrease in the accessibility of healthcare services [ 42 , 43 ], resulting in the underutilization of essential medical insurance funds, leading to resource wastage and diminished efficiency. Maintaining a moderate level of accumulated fund surplus contributes to enhancing the financial robustness of the fund, ensuring its stability when faced with sudden increases in healthcare expenses or other emergencies. In turn, this supports the sustainability of the fund. Furthermore, the rise in accumulated fund surplus also provides greater flexibility for healthcare insurance, such as expanding coverage or improving service quality, thereby enhancing the fund’s efficiency and service levels and benefiting a larger population.

Per capita fund balance is negatively correlated with the operational efficiency of URRBMI and UEBMI. The outbreak and widespread prevalence of COVID-19 at the end of 2019 led to a decrease in the accessibility of healthcare services [ 42 , 43 ], resulting in the underutilization of basic medical insurance funds, leading to resource wastage and diminished efficiency. However, per capita cumulative fund balance exhibits a positive correlation with URRBMI. Maintaining a moderate level of accumulated fund surplus contributes to enhancing the financial robustness of the fund, ensuring its stability when faced with sudden increases in healthcare expenses or other emergencies. In turn, supports the sustainability of the fund. Furthermore, the increase in accumulated fund surplus also provides greater flexibility for healthcare insurance, such as expanding coverage or improving service quality, thereby enhancing the fund’s efficiency and service levels, benefiting a larger population.

The UEBMI fund’s operational efficiency decreases as healthcare facility density rises. This tendency may be explained by the fact that beneficiaries of the UEBMI receive higher actual reimbursement rates for inpatient care than those whose insurance is provided by the URRBMI. As a result, participants in the UEBMI program may experience problems with excessive use of medical services, which wastes medical resources and makes insurance administration more difficult. In turn, the UEBMI’s operational effectiveness suffers as a result.

Against the backdrop of the COVID-19 outbreak and the proactive efforts of the Gansu Provincial Medical Insurance Bureau to promote the level of pooling of basic medical insurance, this study used the DEA-Malmquist-Tobit model to objectively and scientifically evaluate the operational efficiency. The findings of this study hold value for policymakers and healthcare insurance management agencies in formulating and improving policies. However, this study does have certain limitations. Firstly, the Gansu Provincial Medical Insurance Bureau was established in November 2018. Consequently, this study analyzed data on the operation of the basic medical insurance fund only for the years 2020 to 2022. The relatively short period may impact the long-term trends and stability of the research findings. Future studies may benefit from considering a broader time range. Secondly, this research predominantly focused on the Gansu region of China, potentially limiting the generalizability of the results. This limitation restricts the ability to make broad inferences to other areas. Therefore, future research could explore comparisons between multiple regions to gain a more comprehensive understanding of the variations and commonalities in the operational efficiency of healthcare insurance funds. In summary, despite these limitations, this study provides valuable insights into the operational efficiency of the medical insurance fund in Gansu Province. It serves as a beneficial reference for future research and policy formulation.

Conclusions and policy recommendations

Conclusions.

In this study, we conducted a comprehensive analysis of the operational efficiency of the basic medical insurance system in Gansu Province over the past three years using the DEA model, Malmquist total factor productivity index, and Tobit model. Fund revenue, the number of healthcare professionals per 10,000 population, and the number of insured individuals were considered as input indicators. Fund expenditure and hospitalization rate were taken as output indicators. The main findings of the study are summarized below:

By comparing the operational efficiency of URRBMI and UEBMI, as well as the efficiency of UEBMI before and after the enhancement of the pooling level, this study revealed that URRBMI outperforms UEBMI in terms of average efficiency and stability in fund operation. It is noteworthy that the operational efficiency of UEBMI experienced a significant decline from 2020 to 2021. However, after the implementation of municipal-level pooling at the end of 2021, its efficiency showed improvement. Therefore, the study concludes that enhancing the pooling level can effectively improve the operational efficiency and risk resistance of the basic medical insurance system.

From the perspective of financial management of medical insurance funds, an analysis of the influencing factors of URRBMI and UEBMI revealed a negative correlation between per capita fund balance and the operational efficiency of both systems. However, the per capita cumulative fund balance is positively correlated with the operational efficiency of URRBMI. Consequently, the study concludes that financial management of medical insurance funds is a crucial factor influencing the operational efficiency of basic medical insurance.

Regarding the incentive mechanism of basic medical insurance, the analysis in this study indicates a positive correlation between the operational efficiency of URRBMI and the actual reimbursement ratio for hospitalized patients. Thus, the study suggests that the operational efficiency of URRBMI is significantly influenced by the incentive mechanism of basic medical insurance.

From the perspective of healthcare service costs, the study found a negative correlation between per capita hospitalization costs and the operational efficiency of URRBMI. Consequently, the study concludes that high healthcare service costs will lead to a decrease in the efficiency of URRBMI.

Policy recommendations

Based on the conclusions drawn from our study, the following recommendations are proposed:

(1) Control the Growth of Per Capita Hospitalization Costs :

The increase in per capita hospitalization costs has adversely impacted the operational efficiency of the fund. Therefore, it is recommended that healthcare insurance management authorities strengthen their monitoring of healthcare service prices and quality, while actively promoting the implementation of tiered diagnosis and treatment policies. This will contribute to curtailing the unnecessary escalation of per capita hospitalization costs, thereby enhancing the efficiency of the fund.

(2) Strengthen Financial Management of the Fund :

The rise in per capita fund surplus has had unfavorable effects on fund efficiency. Hence, close attention to the financial status of the fund is warranted. Healthcare insurance management authorities may consider formulating rational fund utilization policies to ensure funds are allocated to meet the medical needs of the insured while maintaining an appropriate fund surplus for unforeseen circumstances. This approach will ensure the judicious use of funds and long-term sustainability.

(3) Optimize the Basic Medical Insurance Incentive Mechanism :

The positive impact of an increased actual reimbursement ratio on fund operational efficiency is noted. Therefore, it is suggested to implement tiered diagnosis and treatment policies and judiciously raise the actual reimbursement ratio for hospitalized patients within reasonable limits. This measure will incentivize healthcare service providers to deliver more efficient and economical medical services, contributing to the optimization of the basic medical insurance operational framework.

(4) Elevate Coordination Levels Further Upon Improving Municipal-Level Integration of Basic Medical Insurance :

Our study reveals that elevating coordination levels significantly benefits the operational efficiency and risk resilience of the basic medical insurance fund. Consequently, it is recommended that Gansu Province, building upon improvements in municipal-level integration, actively advances provincial-level integration of basic medical insurance to further enhance the overall efficiency of the insurance system. This proactive step will better equip the system to cope with risks and elevate the overall effectiveness of the medical insurance system.

Data availability

The dataset used during the current study is available from the corresponding author on reasonable request.

Abbreviations

Data Envelopment Analysis

Urban and rural residents’ basic medical insurance

Urban employees’ basic medical insurance

Decision-making units

total efficiency

pure technical efficiency

scale efficiency

Efficiency change

Technical change

Pure efficiency change

Scale efficiency change

Total factor productive efficiency change

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Acknowledgements

We are greatly grateful to the participants and staffs involved in building the resource. Data used for this study can be accessed by contacting the Gansu Provincial Medical Insurance Service Centre.

This research received financial support from the Gansu Provincial Medical Insurance Service Centre (Study on provincial pooling of medical insurance, Grant Number: 20230113).

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F.H.: Conceived and designed the study, collected and analyzed data, and wrote the initial draft of the manuscript.L.H.: Contributed to data collection, conducted statistical analysis, and critically revised the manuscript for important intellectual content.C.W.: Participated in the study’s design, provided expertise in data interpretation, and contributed to manuscript writing and revision.W.X.: Contributed to the study design, and helped finalize the manuscript for submission.L.Q.: Assisted with data collection and analysis, reviewed the manuscript, and provided valuable input for intellectual content.H.X.: Conceived and designed the study, and oversight of the study, and critically reviewed and edited the manuscript.All authors have read and approved the final version of the manuscript. They have agreed to be accountable for all aspects of the work, ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

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Hu, F., Heming, L., Wenxuan, C. et al. Enhancing pooling levels strengthens the risk resilience of healthcare insurance: a case study of basic medical insurance fund operations data in Gansu, China. BMC Public Health 24 , 1129 (2024). https://doi.org/10.1186/s12889-024-18558-y

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Supply chain finance (SCF) solutions open financing channels for small and medium-sized suppliers. However, in uncertain market conditions, payment defaults by supply chain members may affect SCF systems sustainability. To mitigate default risks, financial service providers utilize loan credit insurance (LCI) to transfer the risk to insurers. LCI, purchased by lenders, covers unpaid losses resulting from debtor insolvency, bankruptcy, or political upheaval. In case retailers fail to meet payment obligations, insurers will compensate the lender within the policy terms. Using a game-theoretical approach, we examine LCI’s value for lenders and capital-constrained suppliers. We find that lenders benefit from LCI with higher insurance deductibles and lower insurer loading factors. Moreover, capital-constrained suppliers with higher capital investments and lower production costs can benefit from LCI. Furthermore, suppliers are more likely to obtain extra profits when the insurance scale and loading factor are relatively low. However, when the insurance scale and loading factor are relatively high, the supplier’s capacity investment efficiency is greater. Numerical analysis indicates that LCI with relatively high coverage is advantageous for lenders, particularly full coverage. Another numerical finding is that when the insurance scale is large and the loading factor is high, suppliers achieve greater cost contribution efficiency. Our study highlights LCI’s value in capital-constrained supply chains, benefiting both lenders and suppliers by enhancing profits and encouraging suppliers to increase capital investment and reduce costs. It underscores the role of lender-purchased credit insurance in SCF risk management, providing theoretical support and practical guidance for LCI implementations in commercial financial institutions.

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Acknowledgements

All the authors contributed equally to this work. All the authors are co-first authors of this paper. The authors are grateful to the editors and referees for their valuable comments and suggestions to improve the quality and presentation of the paper. This work is supported by National Natural Science Foundation of China (72271252, 71872200, 71901229), General Project of Shaanxi Provincial Philosophy and Social Sciences Major Theoretical and Practical Issues Research (2022ND0185), Youth Scholar Support Project of Central University of Finance and Economics(QYP2206), and Graduate Academic Incubation Program of Central University of Finance and Economics (202302).

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Appendices: Proofs

1.1 proof of lemma 1.

According to Eq. ( 2 ) and taking the first-order derivative of \(\Pi _s\) with respect to q , we obtain

Subsequently, according to the supplier’s first-order condition (FOC), let \(d\Pi _s/dq=0\) ; we then have \(w (1-r) \bar{F}\left( q\right) =c \bar{F}\left( {\hat{x}}_3\right) .\) We can prove that \(\bar{F}\left( q\right) < \bar{F}\left( {\hat{x}}_3\right) \) because \(F\left( \cdot \right) \) is a strictly increasing function and \(q > B/w\) . Thus, \(c< w (1-r) < w\) .

Furthermore, by taking the second-order derivative of \(\Pi _s\) with respect to q , we have

By substituting the supplier’s FOC into \({d^2\Pi _s}/{dq^2}\) , we have

Based on the IFR assumption of the demand function, we have \(h\left( \hat{x}_3\right) < h\left( q\right) \) because \(\hat{x}_3 < q\) . We have derived that \(w (1-r) > c\) , thus, we have \({d^2\Pi _s}/{dq^2}<0\) — \(\Pi _s\) is a concave function in terms of q at \(d\Pi _s/dq=0\) . Therefore, the supplier’s best response under the given w and r is

1.2 Proof of Lemma 2

According to Eq. ( 3 ), and the end of Eq. ( A.1 ), by taking the first-order derivative of \(\Pi _r\) with respect to w yields

we denote \(\Omega _1=\frac{\partial q^*}{\partial w}\) . By differentiating both sides of Eq.( A.1 ) with respect to w , we have

where \(\frac{\partial \hat{x}_3}{\partial w}=\left( \frac{c}{1-r}\Omega _1-\frac{B}{w}\right) /w\) , Substituting the supplier’s FOC for simplicity, we have

Based on the properties of the IFR distribution, we have \(1-H\left( {\hat{x}}_3\right) > 0\) . As we have proven that \(w (1-r) > c\) and \(h\left( \hat{x}_3\right) < h\left( q\right) \) in the proof of Lemma  1 , we obtain \(w h\left( q^*\right) -c h\left( {\hat{x}}_3\right) /(1-r)>0\) . Therefore, \(\Omega _1=\frac{\partial q^*}{\partial w}>0\) .

Subsequently, according to FOC and letting \(d\Pi _r/dw=0\) , the retailer’s optimal procurement price satisfies

1.3 Proof of Lemma 3

Similar to the proof of Lemma  2 , according to Eq. ( 4 ), and Eq. ( A.1 ), taking the first-order derivative of \(\Pi _f\) with respect to r yields

where \(\frac{\partial B}{\partial r}= \frac{c}{1-r} \frac{\partial q^*}{\partial r} + \frac{B}{1-r}\) .

For notational simplification, we denote \(\Omega _2=\frac{\partial B}{\partial r}\) and \(\Omega _3=\frac{\partial q^*}{\partial r}\) . By differentiating both sides of Eq.( A.1 ) with respect to r , we have

Substituting the supplier’s FOC for simplicity, we have

Subsequently, according to the supplier’s FOC condition and letting \({d\Pi _f}/{dr}=0\) , the lender’s optimal interest rate satisfies

1.4 Proof of Corollary 1

Based on \(\Omega _1\) and \(\Omega _3\) that we deduced in the proof of Lemma  2 and Lemma  3 , we find the denominators of \(\Omega _1\) and \(\Omega _3\) have the opposite sign because \(\Omega _1=-(1-r)\Omega _3/w\) . In the proof of Lemma  2 , we have \(\Omega _1>0\) . Thus, we can easily verify \(\Omega _3=\frac{\partial q^*}{\partial r}<0\) .

Substituting the formula of \(\Omega _3\) into \(\Omega _2=\frac{\partial B}{\partial r}= \frac{c}{1-r} \frac{\partial q^*}{\partial r} + \frac{B}{1-r}\) , we have

Based on the properties of the IFR distribution, we have \(1-H(q^*) > 0\) . Since we have proved that \(w (1-r) > c\) and \(h\left( \hat{x}_3\right) < h\left( q\right) \) in the proof of Lemma  1 , we obtain \(ch\left( \hat{x}_3\right) /w-(1-r)h(q^*)<0\) . Thus, we have \(\Omega _2=\frac{\partial B}{\partial r}<0\) . Next, we simplify Eq.( A.3 ) into \(B=\Omega _2 \{F\left( \hat{x}_3\right) -\theta \left[ F\left( \hat{x}_1\right) -F\left( \hat{x}_2\right) \right] -r^*\}\) . We can deduce that \(F\left( \hat{x}_3\right) -\theta \left[ F\left( \hat{x}_1\right) -F\left( \hat{x}_2\right) \right] -r^*<0\) because \(\Omega _2<0\) and \(B>0\) hold. Since \(\hat{x}_1<\hat{x}_2\) and the increasing demand CDF, we have \(F\left( \hat{x}_1\right) -F\left( \hat{x}_2\right) <0\) . Thus, we obtain the restriction for the loading factor, \(\theta < \frac{r^*-F\left( \hat{x}_3\right) }{F\left( \hat{x}_2\right) -F\left( \hat{x}_1\right) }\) .

Taking the partial derivative with respect to k on both sides of Eq.( A.1 ), we have

. Additionally, substituting Eq.( A.1 ) into the above formula and simplifying, we have

Therefore, we have \( {\partial q^*}/{\partial k} <0\) for \(h\left( \hat{x}_3\right) >0\) and \(ch\left( \hat{x}_3\right) -w(1-r)h(q^*)<0\) .

1.5 Proof of Proposition 1

According to Eq. ( 4 ) and the lender’s profit function in the benchmark, we calculate the lender’s profit difference between the LCI scheme and benchmark.

For notational simplification, let \(Y(x)=\int ^x_0 F(x)dx\) , which is a monotonically increasing function because \(dY(x)/dx=F(x)>0\) . Thus, the necessary condition for the lender to benefit from LCI (i.e., \(\Delta \Pi _f \ge 0\) ) is

The condition Eq. ( A.4 ) can be rewritten as \(Y\left( \hat{x}_2\right) <\frac{1}{\theta w^*}\mathscr {A}_1+Y\left( \hat{x}_1\right) \) . If \(\frac{1}{\theta w^*}\mathscr {A}_1+Y\left( \hat{x}_1\right) \ge 0\) , we have \(\hat{x}_2<Y^{-1}\left[ \frac{1}{\theta w^*}\mathscr {A}_1+Y\left( \hat{x}_1\right) \right] \) since \(Y^{-1}(x)\) has the same monotonicity as Y ( x ). Thus, the condition can be simplified to \(d>B-w^*Y^{-1}\left[ \frac{1}{\theta w^*}\mathscr {A}_1+Y\left( \hat{x}_1\right) \right] \) . If \(\frac{1}{\theta w^*}\mathscr {A}_1+Y\left( \hat{x}_1\right) <0\) , this condition does not hold because \(Y\left( \hat{x}_2\right) \ge 0 > \frac{1}{\theta w^*}\mathscr {A}_1+Y\left( \hat{x}_1\right) \) .

Hence, let \(\mathscr {A}_1={\left[ Br^*-w^*Y\left( {\hat{x}}_3\right) -{B^N}{r^N}^*+w^*Y\left( {\hat{x}}^N_3\right) \right] }/{w^*\theta }+Y\left( {\hat{x}}_1\right) \) , if \(\mathscr {A}_1 \ge 0\) . There exists a threshold

for which \(d\ge \hat{d}\) is the value of LCI for the lender \(\Delta \Pi _f \ge 0\) . Otherwise, the value of LCI for the lender is \(\Delta \Pi _f < 0\) .

From the perspective of the loading factor, Eq. ( A.4 ) can be rewritten as \(w^*\theta \left[ Y\left( \hat{x} _2\right) -Y\left( \hat{x} _1\right) \right] \le Br^*- w^*Y\left( {\hat{x}} _3\right) -{B^N}{r^N} ^*+w{N^*} Y\left( {\hat{x}} ^N_3\right) \) . Clearly, \(\left[ Y\left( \hat{x}_2\right) -Y\left( \hat{x}_1\right) \right] >0\) because \(\hat{x}_2>\hat{x}_1\) . Then, the value-added condition can be simplified as \(\theta \le \frac{Br^*- w^*Y\left( {\hat{x}} _3\right) -{B^N}{r^N} ^*+w^{N*} Y\left( {\hat{x}} ^N_3\right) }{w^* \left[ Y\left( \hat{x} _2\right) -Y\left( \hat{x} _1\right) \right] }\) . Therefore, there exists a threshold

When \(\theta \le \hat{\theta }\) , the value of LCI for the lender is \(\Delta \Pi _f \ge 0\) . Otherwise, when \(\theta > \hat{\theta }\) , the value of LCI for the lender is \(\Delta \Pi _f < 0\) .

1.6 Proof of Proposition 2

According to Eq. ( 2 ) and the supplier’s profit function in the benchmark, and calculating the supplier’s profit difference between the LCI scheme and the benchmark, we obtain

To simplify the notation, let \(S(x)=\int ^x_0 \bar{F}(x)dx\) be a monotonically increasing function because \(dS(x)/dx=\bar{F}(x)>0\) . Thus, the necessary condition for the supplier to benefit from LCI (i.e., \(\Delta \Pi _s \ge 0\) ) is

If \({w^N}^* S\left( \hat{x}_3^N\right) +w^* S\left( q^*\right) - {w^N}^* S\left( {q^N}^*\right) \ge 0\) , Eq. ( A.5 ) can be rewritten as \(B \le w^* S^{-1}\{S(q^*)-\frac{{w^N}^*}{w^*} \left[ S\left( {q^N}^*\right) -S\left( \hat{x}_3^N\right) \right] \}\) since \(S^{-1}(x)\) has the same monotonicity as S ( x ). Thus, \(k \ge cq^*-(1-r^*)w^* S^{-1}\{S(q^*)-\frac{{w^N}^*}{w^*} \left[ S\left( {q^N}^*\right) -S\left( \hat{x}_3^N\right) \right] \}\) . If \({w^N}^* S\left( \hat{x}_3^N\right) +w^* S\left( q^*\right) - {w^N}^* S\left( {q^N}^*\right) < 0\) ; the condition in Eq.( A.5 ) does not hold, because \(S\left( \hat{x}_3\right) \ge 0 > {w^N}^* S\left( \hat{x}_3^N\right) +w^* S\left( q^*\right) - {w^N}^* S\left( {q^N}^*\right) \) .

Hence, let \(\mathscr {A}_2=S(q^*)-\frac{{w^N}^*}{w^*} \left[ S\left( {q^N}^*\right) -S\left( \hat{x}_3^N\right) \right] \) . If \(\mathscr {A}_2 \ge 0\) , there exists a threshold

that satisfies \(cq^*-\hat{k}>0\) . When \(k\ge \hat{k}\) , the value of LCI for the supplier \(\Delta \Pi _s \ge 0\) . Otherwise, the value of LCI for the supplier \(\Delta \Pi _s < 0\) .

1.7 Proof of Corollary 2

From the lender’s FOC condition in Eq. ( A.3 ), we have

Subsequently, substituting the equation above into the expression of \(\hat{k}\) , we have

Taking the derivative of \(\hat{k}\) with respect to b yields

Thus, we can verify \(\frac{\partial \hat{k}}{\partial b}>0\) because \(S^{-1}\left( \mathscr {A}_2\right) >0\) .

Taking the derivative of \(\hat{k}\) with respect to d yields

Thus, it is easy to verify that \(\frac{\partial \hat{k}}{\partial d}<0\) .

Taking the derivative of \(\hat{k}\) with respect to \(\theta \) yields

Therefore, we can deduce that \(\frac{\partial \hat{k}}{\partial \theta }>0\) because we have proved \(\bar{F}\left( \hat{x}_1\right) -\bar{F}\left( \hat{x}_2\right) >0\) .

1.8 Proof of Corollary 3

Based on our definition, we have \(\eta =\frac{d{\Pi _s}^*}{dk}=\frac{\partial {\Pi _s}^*}{\partial q^*}\frac{dq^*}{dk}+\frac{\partial {\Pi _s}^*}{\partial k}\) . According to the supplier’s FOC condition, the supplier’s optimal response \(q^*\) satisfies \(\frac{\partial {\Pi _s}^*}{\partial q^*}=0\) . Thus, we have \(\eta =\frac{\partial {\Pi _s}^*}{\partial k}=\frac{1}{1-r^*} \bar{F}\left( \hat{x}_3\right) \) . Substituting Eq.( A.3 ) into the above formula, we have

Taking the derivative of \(\eta \) with respect to b yields

1.9 Proof of Proposition 3

From the perspective of the supplier’s unit production cost and based on the supplier’s positive value condition in Eq. ( A.5 ), we have \(B \le w^* S^{-1}\{S(q^*)-\frac{{w^N}^*}{w^*} \left[ S\left( {q^N}^*\right) -S\left( \hat{x}_3^N\right) \right] \}\) , which implies that \(c \le \left[ (1-r^*) w^*S^{-1}\left( \mathscr {A}_2\right) +k\right] /q^* \) . Therefore, if \(\mathscr {A}_2 \ge 0\) , we obtain the threshold

satisfying \(\hat{c}q^*-k>0\) . When \(c\le \hat{c}\) , the value of LCI for the supplier \(\Delta \Pi _s \ge 0\) . Otherwise, the value of LCI for the supplier \(\Delta \Pi _s < 0\) .

1.10 Proof of Corollary 4

Based on the proof of Corollary  2 , we have \(1-r^*{=}B/\Omega _2+\bar{F}\left( \hat{x}_3\right) -\theta \left[ \bar{F}\left( \hat{x}_1\right) {-}\bar{F}\left( \hat{x}_2\right) \right] \) . Subsequently, substituting the equation above into the expression of \(\hat{c}\) , we have

Taking the derivative of \(\hat{c}\) with respect to b yields

Thus, we can verify \(\frac{\partial \hat{c}}{\partial b}<0\) because \(S^{-1}\left( \mathscr {A}_2\right) >0\) .

Taking the derivative of \(\hat{c}\) with respect to d yields

Thus, it is easy to verify that \(\frac{\partial \hat{c}}{\partial d}>0\) .

Taking the derivative of \(\hat{c}\) with respect to \(\theta \) yields

Therefore, we can deduce that \(\frac{\partial \hat{c}}{\partial \theta }<0\) because we have proved that \(\bar{F}\left( \hat{x}_1\right) -\bar{F}\left( \hat{x}_2\right) >0\) .

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Zhong, H., Yan, N., Lu, J. et al. Value of loan credit insurance in the capital-constrained supply chain. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-05976-9

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Received : 17 August 2023

Accepted : 26 March 2024

Published : 22 April 2024

DOI : https://doi.org/10.1007/s10479-024-05976-9

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