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Optimal insurance with background risk: An analysis of general dependence structures

Author

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  • Yichun Chi

    (Central University of Finance and Economics)

  • Wei Wei

    (University of Wisconsin-Milwaukee)

Abstract

In this paper, we consider an optimal insurance problem from the perspective of a risk-averse individual who faces an insurable risk as well as some background risk and wants to maximise the expected utility of his/her final wealth. To reduce ex post moral hazard, we follow Huberman et al. (Bell J. Econ. 14:415–426 1983) to assume that alternative insurance contracts satisfy the principle of indemnity and the no-sabotage condition. When the insurance premium is calculated by the expected value premium principle, a necessary and sufficient condition for the optimality of an insurance contract is established under a general dependence structure between insurable and background risks. By virtue of this condition, some qualitative properties of optimal contracts are developed, a scheme is provided to improve any suboptimal insurance strategy, and optimal insurance forms are derived explicitly for some dependence structures of interest. These forms are not always piecewise linear.

Suggested Citation

  • Yichun Chi & Wei Wei, 2020. "Optimal insurance with background risk: An analysis of general dependence structures," Finance and Stochastics, Springer, vol. 24(4), pages 903-937, October.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:4:d:10.1007_s00780-020-00429-0
    DOI: 10.1007/s00780-020-00429-0
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    References listed on IDEAS

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    Cited by:

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    4. Yichun Chi & Xun Yu Zhou & Sheng Chao Zhuang, 2020. "Variance Contracts," Papers 2008.07103, arXiv.org.
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    6. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2022. "Risk transference constraints in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 27-40.
    7. Chi, Yichun & Zhuang, Sheng Chao, 2022. "Regret-based optimal insurance design," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 22-41.
    8. Vincent, Léonard & Albrecher, Hansjörg & Krvavych, Yuriy, 2021. "Structured reinsurance deals with reference to relative market performance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 125-139.
    9. Sun, Huan & Wang, Haiyan & Steffensen, Sonja, 2022. "Mechanism design of multi-strategy health insurance plans under asymmetric information," Omega, Elsevier, vol. 107(C).
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    More about this item

    Keywords

    Background risk; General dependence structures; Mossin’s theorem; No-sabotage condition; Optimal insurance design;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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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