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Revisiting the optimal insurance design under adverse selection: Distortion risk measures and tail-risk overestimation

Author

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  • Liang, Zhihang
  • Zou, Jushen
  • Jiang, Wenjun

Abstract

This paper studies the design of optimal insurance from an insurer's perspective when it is subject to adverse selection issue. Different from the literature, the insureds who are exposed to different types of risks are allowed to apply different preference measures. By assuming that the insureds' preferences are dictated by some distortion risk measures that always over-estimate the tail risk, we figure out the optimal policy menu without assuming the parametric form of indemnity functions. We also find that the insureds who deem their losses riskier than those of others will always purchase full insurance, which is consistent with the results in past studies. Furthermore, we show that in the presence of adverse selection the optimal policy menu always outperforms the optimal single policy in the sense that the former can yield a larger expected profit for the insurer. This outcome also echoes some existing results in the literature.

Suggested Citation

  • Liang, Zhihang & Zou, Jushen & Jiang, Wenjun, 2022. "Revisiting the optimal insurance design under adverse selection: Distortion risk measures and tail-risk overestimation," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 200-221.
    • Handle: RePEc:eee:insuma:v:104:y:2022:i:c:p:200-221
    DOI: 10.1016/j.insmatheco.2022.03.002
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    Citations

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    Cited by:

    1. Zhu, Michael B. & Ghossoub, Mario & Boonen, Tim J., 2023. "Equilibria and efficiency in a reinsurance market," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 24-49.
    2. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2023. "Optimal Insurance: Dual Utility, Random Losses and Adverse Selection," ECONtribute Discussion Papers Series 242, University of Bonn and University of Cologne, Germany.

    More about this item

    Keywords

    Optimal insurance; Distortion risk measure; Adverse selection; Individual rationality; Separation compatibility;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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