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Optimal Insurance Under the Insurer's VaR Constraint

Author

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  • Chunyang Zhou

    (Financial Engineering Research Center, Shanghai Jiao Tong University, No. 535, Fahuazhen Road, Shanghai, China)

  • Chongfeng Wu

    (Financial Engineering Research Center, Shanghai Jiao Tong University, No. 535, Fahuazhen Road, Shanghai, China)

Abstract

In this paper, we impose the insurer's Value at Risk (VaR) constraint on Arrow's optimal insurance model. The insured aims to maximize his expected utility of terminal wealth, under the constraint that the insurer wishes to control the VaR of his terminal wealth to be maintained below a prespecified level. It is shown that when the insurer's VaR constraint is binding, the solution to the problem is not linear, but piecewise linear deductible, and the insured's optimal expected utility will increase as the insurer becomes more risk-tolerant. Basak and Shapiro (2001) showed that VaR risk managers often choose larger risk exposures to risky assets. We draw a similar conclusion in this paper. It is shown that when the insured has an exponential utility function, optimal insurance based on VaR constraint causes the insurer to suffer larger losses than optimal insurance without insurer's risk constraint.

Suggested Citation

  • Chunyang Zhou & Chongfeng Wu, 2009. "Optimal Insurance Under the Insurer's VaR Constraint," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 34(2), pages 140-154, December.
    • Handle: RePEc:pal:genrir:v:34:y:2009:i:2:p:140-154
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    Cited by:

    1. Jiang, Wenjun & Hong, Hanping & Ren, Jiandong, 2021. "Pareto-optimal reinsurance policies with maximal synergy," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 185-198.
    2. Wang, Ching-Ping & Huang, Hung-Hsi, 2016. "Optimal insurance contract under VaR and CVaR constraints," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 110-127.
    3. Ghossoub, Mario & Jiang, Wenjun & Ren, Jiandong, 2022. "Pareto-optimal reinsurance under individual risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 307-325.

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