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Optimal Insurance Contracts Under Distortion Risk Measures With Ambiguity Aversion

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  • Jiang, Wenjun
  • Escobar-Anel, Marcos
  • Ren, Jiandong

Abstract

This paper presents analytical representations for an optimal insurance contract under distortion risk measure and in the presence of model uncertainty. We incorporate ambiguity aversion and distortion risk measure through the model of Robert and Therond [(2014) ASTIN Bulletin: The Journal of the IAA, 44(2), 277–302.] as per the framework of Klibanoff et al. [(2005) A smooth model of decision making under ambiguity. Econometrica, 73(6), 1849–1892.]. Explicit optimal insurance indemnity functions are derived when the decision maker (DM) applies Value-at-Risk as risk measure and is ambiguous about the loss distribution. Our results show that: (1) under model uncertainty, ambiguity aversion results in a distorted probability distribution over the set of possible models with a bias in favor of the model which yields a larger risk; (2) a more ambiguity-averse DM would demand more insurance coverage; (3) for a given budget, uncertainties about the loss distribution result in higher risk level for the DM.

Suggested Citation

  • Jiang, Wenjun & Escobar-Anel, Marcos & Ren, Jiandong, 2020. "Optimal Insurance Contracts Under Distortion Risk Measures With Ambiguity Aversion," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 619-646, May.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:2:p:619-646_10
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    Cited by:

    1. John A. Major & Stephen J. Mildenhall, 2020. "Pricing and Capital Allocation for Multiline Insurance Firms With Finite Assets in an Imperfect Market," Papers 2008.12427, arXiv.org.
    2. Bradley, Richard, 2024. "Catastrophe insurance decision making when the science is uncertain," LSE Research Online Documents on Economics 122508, London School of Economics and Political Science, LSE Library.
    3. Cong Tam Trinh & Xuan Nguyen & Pasquale Sgro, 2021. "Culture and the demand for non‐life insurance: Empirical evidences from middle‐income and high‐income economies," Economics of Transition and Institutional Change, John Wiley & Sons, vol. 29(3), pages 431-458, July.
    4. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    5. Boonen, Tim J. & Jiang, Wenjun, 2022. "A marginal indemnity function approach to optimal reinsurance under the Vajda condition," European Journal of Operational Research, Elsevier, vol. 303(2), pages 928-944.
    6. Liu, Haiyan & Mao, Tiantian, 2022. "Distributionally robust reinsurance with Value-at-Risk and Conditional Value-at-Risk," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 393-417.
    7. Wei Wang & Huifu Xu, 2023. "Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making," Computational Management Science, Springer, vol. 20(1), pages 1-51, December.
    8. Boonen, Tim J. & Jiang, Wenjun, 2024. "Robust insurance design with distortion risk measures," European Journal of Operational Research, Elsevier, vol. 316(2), pages 694-706.

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