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Optimal insurance design of ambiguous risks

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  • Christian Gollier

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Abstract

We examine the characteristics of the optimal insurance contract under linear transaction costs and an ambiguous distribution of losses. Under the standard expected utility model, we know from Arrow ( 1965 ) that it contains a straight deductible. In this paper, we assume that the policyholder is ambiguity averse in the sense of Klibanoff et al. (Econometrica 73(6):1849–1892, 2005 ). The optimal contract depends upon the structure of the ambiguity. For example, if the set of possible priors can be ranked according to the monotone likelihood ratio order, the optimal contract contains a disappearing deductible. We also show that the policyholder’s ambiguity aversion may have the counterintuitive effect to reduce the optimal insurance coverage of an ambiguous risk. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
  • Handle: RePEc:spr:joecth:v:57:y:2014:i:3:p:555-576
    DOI: 10.1007/s00199-014-0845-8
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    File URL: http://hdl.handle.net/10.1007/s00199-014-0845-8
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    3. Christophe Courbage & Beatrice Rey, 2016. "On ambiguity apportionment," Journal of Economics, Springer, vol. 118(3), pages 265-275, July.
    4. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2020. "Optimal Insurance under Maxmin Expected Utility," Papers 2010.07383, arXiv.org.
    5. Louis Eeckhoudt & Liqun Liu & Jack Meyer, 2017. "Restricted increases in risk aversion and their application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 161-181, June.
    6. Dietz, Simon & Walker, Oliver, 2017. "Ambiguity and insurance: capital requirements andpremiums," LSE Research Online Documents on Economics 68469, London School of Economics and Political Science, LSE Library.
    7. Luciano I. Castro & Zhiwei Liu & Nicholas C. Yannelis, 2017. "Ambiguous implementation: the partition model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 233-261, January.
    8. Massimiliano Amarante & Mario Ghossoub, 2016. "Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer," Risks, MDPI, Open Access Journal, vol. 4(1), pages 1-27, March.
    9. Lu, Zhiyi & Meng, Shengwang & Liu, Leping & Han, Ziqi, 2018. "Optimal insurance design under background risk with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 15-28.
    10. Mingli Zheng & Chong Wang & Chaozheng Li, 2016. "Insurance Contracts with Adverse Selection When the Insurer Has Ambiguity about the Composition of the Consumers," Annals of Economics and Finance, Society for AEF, vol. 17(1), pages 179-206, May.
    11. Marie-Charlotte Guetlein, 2016. "Comparative Risk Aversion in the Presence of Ambiguity," American Economic Journal: Microeconomics, American Economic Association, vol. 8(3), pages 51-63, August.
    12. Richard J. Arend, 2020. "Strategic decision-making under ambiguity: a new problem space and a proposed optimization approach," Business Research, Springer;German Academic Association for Business Research, vol. 13(3), pages 1231-1251, November.
    13. Birghila, Corina & Pflug, Georg Ch., 2019. "Optimal XL-insurance under Wasserstein-type ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 30-43.
    14. Yaoyao Wu & Jinqiang Yang & Zhentao Zou, 2018. "Ambiguity sharing and the lack of relative performance evaluation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 141-157, July.
    15. Mario Ghossoub, 2016. "Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-28, August.
    16. Kit Pong Wong, 2015. "A Smooth Ambiguity Model Of The Competitive Firm," Bulletin of Economic Research, Wiley Blackwell, vol. 67(S1), pages 97-110, December.
    17. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    18. Zheng, Jiakun, 2020. "Optimal insurance design under narrow framing," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 596-607.
    19. Biener, Christian & Landmann, Andreas & Santana, Maria Isabel, 2019. "Contract nonperformance risk and uncertainty in insurance markets," Journal of Public Economics, Elsevier, vol. 175(C), pages 65-83.
    20. Huang, Rachel J. & Huang, Yi-Chieh & Tzeng, Larry Y., 2013. "Insurance bargaining under ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 812-820.
    21. Hu, Duni & Chen, Shou & Wang, Hailong, 2018. "Robust reinsurance contracts with uncertainty about jump risk," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1175-1188.
    22. Jiang, Wenjun & Ren, Jiandong & Yang, Chen & Hong, Hanping, 2019. "On optimal reinsurance treaties in cooperative game under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 173-184.
    23. Peter, Richard & Ying, Jie, 2020. "Do you trust your insurer? Ambiguity about contract nonperformance and optimal insurance demand," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 938-954.

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    More about this item

    Keywords

    Deductible; Risk-sharing; Ambiguity; Monotone likelihood ratio order; D81; G22;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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