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Optimal insurance under multiple sources of risk with positive dependence

Author

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  • Lu, ZhiYi
  • Liu, LePing
  • Zhang, JianYu
  • Meng, LiLi

Abstract

In this paper we try to derive an optimal insurance treaty when the insured faces multiple sources of risk. We show that the deductible insurance is optimal when the insurable and uninsurable risks are positively dependent or independent within the expected utility framework. A necessary condition of optimal deductible is given under some mild conditions. We compare our model with the classical one without background risk. Furthermore, the shifts of optimal deductible and expected utility by modifications of the dependence structure and the marginal are analyzed.

Suggested Citation

  • Lu, ZhiYi & Liu, LePing & Zhang, JianYu & Meng, LiLi, 2012. "Optimal insurance under multiple sources of risk with positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 462-471.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:462-471
    DOI: 10.1016/j.insmatheco.2012.06.011
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    References listed on IDEAS

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    1. repec:hal:journl:hal-00538974 is not listed on IDEAS
    2. Marco Scarsini & Alfred Muller, 2001. "Stochastic comparison of random vectors with a common copula," Post-Print hal-00540198, HAL.
    3. Doherty, Neil A & Schlesinger, Harris, 1983. "The Optimal Deductible for an Insurance Policy When Initial Wealth Is Random," The Journal of Business, University of Chicago Press, vol. 56(4), pages 555-565, October.
    4. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    6. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    7. Soon Koo Hong & Keun Ock Lew & Richard MacMinn & Patrick Brockett, 2011. "Mossin's Theorem Given Random Initial Wealth," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 309-324, June.
    8. Kischka, Peter, 1988. "Aspects of optimal insurance demand when there are uninsurable risks," Insurance: Mathematics and Economics, Elsevier, vol. 7(1), pages 9-14, January.
    9. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    10. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, vol. 133(1), pages 152-176, March.
    11. Van Heerwaarden, A. E. & Kaas, R. & Goovaerts, M. J., 1989. "Optimal reinsurance in relation to ordering of risks," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 11-17, March.
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    Cited by:

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    3. 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.
    4. 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.
    5. Hong Liang, 2020. "On Three Standard Results in the Theory of Insurance Demand," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(1), pages 1-10, January.

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