Risk measures induced by efficient insurance contracts

Qiuqi Wang; Ruodu Wang; Ricardas Zitikis

AI summary · arXiv: 2109.00314v2 · econ.TH

Risk measures induced by efficient insurance contracts

Qiuqi Wang, Ruodu Wang, Ricardas Zitikis

Original paper Submitted to arXiv on 01 Sep. 2021 24 pages License: CC BY-NC-SA 4.0

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The essentials

The Expected Shortfall (ES) is a widely used regulatory risk measure in finance, insurance, and statistics.
There has been a visible gap in justifying the special role of ES in insurance and actuarial science.
A mixture of mean and ES can be characterized as the risk measure for both parties when contracts with deductibles are efficient.
The study also presents characterization results for other risk measures such as distortion risk measures by linking them to different sets of contracts.
ES is not seen to dominate other convex risk measures in the insurance market due to various factors that need to be taken into account.
The authors note that their characterization results can be extended to multi-player cases with multiple insurers and linked to characterization problems in risk-sharing scenarios.
Their findings may have practical applications such as evaluating customer risk attitudes based on provided menus of contracts.
This paper contributes significantly to understanding the role of ES in insurance design and actuarial science.
It highlights how efficient insurance contracts can induce specific types of risk measures and provides avenues for future research using game theoretic approaches or experimental studies to further explore these topics.

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AI-generated keywords: Expected Shortfall Insurance Pareto Optimal Risk Measure Actuarial Science

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Original abstract

The Expected Shortfall (ES) is a widely used regulatory risk measure in finance, insurance, and statistics. However, there has been a visible gap in justifying the special role of ES in insurance and actuarial science. To address this gap, this study focuses on the characterization of risk measures induced by efficient insurance contracts that are Pareto optimal for both the insurer and the insured. One of the major findings of this study is that a mixture of mean and ES can be characterized as the risk measure for both parties when contracts with deductibles are efficient. The study also presents characterization results for other risk measures such as distortion risk measures by linking them to different sets of contracts. While ES is not seen to dominate other convex risk measures in the insurance market due to various factors that need to be taken into account, this research provides additional insights into why ES is a natural choice for insurers when evaluating risks in the insurance market. The authors note that their characterization results can be extended to multi-player cases with multiple insurers and linked to characterization problems in risk-sharing scenarios. Additionally, their findings may have practical applications such as evaluating customer risk attitudes based on provided menus of contracts. Overall, this paper contributes significantly to understanding the role of ES in insurance design and actuarial science. It highlights how efficient insurance contracts can induce specific types of risk measures and provides avenues for future research using game theoretic approaches or experimental studies to further explore these topics.

Exploring the Role of Expected Shortfall in Insurance Design and Actuarial Science

Insurance is a critical component of financial security, providing protection against potential losses due to unforeseen events. As such, it is important for insurers to accurately assess risk when designing insurance contracts. The Expected Shortfall (ES) is a widely used regulatory risk measure in finance, insurance, and statistics that has been found to be particularly useful for evaluating risks in the insurance market. However, there has been a visible gap in justifying the special role of ES in insurance and actuarial science.

To address this gap, this study focuses on the characterization of risk measures induced by efficient insurance contracts that are Pareto optimal for both the insurer and the insured. Through their research, they have identified several key findings regarding ES’s role in assessing risks within an insurance context.

Mixture of Mean and ES as Risk Measure

One major finding from this research was that a mixture of mean and ES can be characterized as the risk measure for both parties when contracts with deductibles are efficient. This means that when designing an optimal contract between an insurer and insured party, taking into account both mean values (average expected loss) as well as ES values (riskiest expected loss) can provide better insight into how much risk each party is exposed to under different scenarios.

Characterization Results for Other Risk Measures

The study also presents characterization results for other risk measures such as distortion risk measures by linking them to different sets of contracts. This suggests that other convex risk measures may be more suitable than ES depending on specific factors related to individual insurers or markets – meaning that while ES may not always dominate other convex risk measures in terms of accuracy or effectiveness, it still plays an important role within certain contexts where its use could prove beneficial over alternative options.

Practical Applications & Future Research Avenues

Additionally, their findings may have practical applications such as evaluating customer risk attitudes based on provided menus of contracts – allowing insurers to better understand which types of policies customers prefer based on their own personal preferences towards various levels or types of risks associated with each option presented. The authors note that their characterization results can be extended to multi-player cases with multiple insurers and linked to characterization problems in risk-sharing scenarios – suggesting potential avenues for future research using game theoretic approaches or experimental studies to further explore these topics.

Conclusion: Significance & Implications

Overall, this paper contributes significantly to understanding the role of ES in insurance design and actuarial science by highlighting how efficient insurance contracts can induce specific types of risk measures while also providing insights into why ES might be preferred over other convex alternatives depending on certain factors related to individual insurers or markets.. It provides valuable information about how best evaluate risks within an insurance context while also offering potential areas for further exploration through additional experiments or theoretical models involving multiple players/insurers operating within shared environments

Created on 11 Jun. 2023

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