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Optimal insurance under the insurer's risk constraint

Listed author(s):
  • Zhou, Chunyang
  • Wu, Chongfeng
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    In this paper, we impose the insurer's risk constraint on Arrow's optimal insurance model. The insured aims to maximize his/her expected utility of terminal wealth, under the constraint that the insurer wishes to control the expected loss of his/her terminal wealth below some prespecified level. We solve the problem, and it is shown that when the insurer's risk constraint is binding, the solution to the problem is not linear, but piecewise linear deductible. Moreover, it can be shown that the insured's optimal expected utility will increase if the insurer increases his/her risk tolerance.

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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 3 (June)
    Pages: 992-999

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:992-999
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    1. Promislow, S.David & Young, Virginia R., 2005. "Unifying framework for optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 347-364, June.
    2. Hung-Hsi Huang, 2006. "Optimal insurance contract under a value-at-risk constraint," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 31(2), pages 91-110, December.
    3. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    4. Gajek, Leslaw & Zagrodny, Dariusz, 2004. "Optimal reinsurance under general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 227-240, April.
    5. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    6. Gajek, Leslaw & Zagrodny, Dariusz, 2000. "Insurer's optimal reinsurance strategies," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 105-112, August.
    7. Zhou, Chunyang & Wu, Chongfeng & Zhang, Shengping & Huang, Xuejun, 2008. "An optimal insurance strategy for an individual under an intertemporal equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 255-260, February.
    8. Ching-Ping Wang & David Shyu & Hung-Hsi Huang, 2005. "Optimal Insurance Design Under a Value-at-Risk Framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 30(2), pages 161-179, December.
    9. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
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