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Reinsurance contract design when the insurer is ambiguity-averse

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  • Hu, Duni
  • Wang, Hailong

Abstract

This paper investigates proportional and excess-loss reinsurance contracts in a continuous-time principal–agent framework, in which the insurer is the agent and the reinsurer is the principal. Insurance claims follow the classic Cramér–Lundberg process. The insurer believes that the claim intensity is uncertain and he chooses robust risk retention levels to maximize the penalty-dependent multiple-priors utility. The reinsurer designs reinsurance contracts subject to the insurer’s incentive compatibility constraints. The analytical expressions of the two robust reinsurance contracts are derived. Our results show that the robust reinsurance demand and price are greater than their respective standard values without model ambiguity, and increase as the insurer’s ambiguity aversion increases. Moreover, the reinsurer specifies a decreasing reinsurance price to induce increasing demand over time. Specifically, the price of excess-loss reinsurance is higher, relative to that of proportional reinsurance. Further, only if the insurer’s risk aversion is high or the reinsurer’s risk aversion is low, the insurer prefers the excess-loss reinsurance contract.

Suggested Citation

  • Hu, Duni & Wang, Hailong, 2019. "Reinsurance contract design when the insurer is ambiguity-averse," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 241-255.
    • Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:241-255
    DOI: 10.1016/j.insmatheco.2019.03.007
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    References listed on IDEAS

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    More about this item

    Keywords

    Ambiguity; Principal–agent model; Proportional reinsurance; Excess-loss reinsurance; Reinsurance price;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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