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Risk measures induced by efficient insurance contracts

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  • Wang, Qiuqi
  • Wang, Ruodu
  • Zitikis, Ričardas

Abstract

The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets of axioms from perspectives of portfolio risk management and statistics. Meanwhile, there is large literature on insurance design with ES as an objective or a constraint. A visible gap is to justify the special role of ES in insurance and actuarial science. To fill this gap, we study the characterization of risk measures induced by efficient insurance contracts, i.e., those that are Pareto optimal for the insured and the insurer. One of our major results is that we characterize a mixture of the mean and ES as the risk measure of the insured and the insurer, when contracts with deductibles are efficient. Characterization results of other risk measures, including the mean and distortion risk measures, are also presented by linking them to different sets of contracts.

Suggested Citation

  • Wang, Qiuqi & Wang, Ruodu & Zitikis, Ričardas, 2022. "Risk measures induced by efficient insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 56-65.
    • Handle: RePEc:eee:insuma:v:103:y:2022:i:c:p:56-65
    DOI: 10.1016/j.insmatheco.2022.01.003
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    References listed on IDEAS

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    More about this item

    Keywords

    Optimal insurance; Expected Shortfall; Pareto optimality; Deductible; Concentration;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G2 - Financial Economics - - Financial Institutions and Services

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