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Optimal insurance design with a bonus

Author

Listed:
  • Li, Yongwu
  • Xu, Zuo Quan

Abstract

This paper investigates an insurance design problem, in which a bonus will be given to the insured if no claim has been made during the whole lifetime of the contract, for an expected utility insured. In this problem, the insured has to consider the so-called optimal action rather than the contracted compensation (or indemnity) due to the existence of the bonus. For any pre-agreed bonus, the optimal insurance contract is given explicitly and shown to be either the full coverage contract when the insured pays high enough premium, or a deductible one otherwise. The optimal contract and bonus are also derived explicitly if the insured is allowed to choose both of them. The contract turns out to be of either zero reward or zero deductible. In all cases, the optimal contracts are universal, that is, they do not depend on the specific form of the utility of the insured. A numerical example is also provided to illustrate the main theoretical results of the paper.

Suggested Citation

  • Li, Yongwu & Xu, Zuo Quan, 2017. "Optimal insurance design with a bonus," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 111-118.
    • Handle: RePEc:eee:insuma:v:77:y:2017:i:c:p:111-118
    DOI: 10.1016/j.insmatheco.2017.09.003
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    References listed on IDEAS

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    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
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    10. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
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    Cited by:

    1. 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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