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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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    Cited by:

    1. Chi, Yichun & Liu, Fangda, 2017. "Optimal insurance design in the presence of exclusion clauses," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 185-195.
    2. 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.
    3. Liu, Ying & Li, Xiaozhong & Liu, Yinli, 2015. "The bounds of premium and optimality of stop loss insurance under uncertain random environments," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 273-278.
    4. 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.
    5. 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.

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