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Dynamic risk-sharing game and reinsurance contract design

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  • Chen, Shumin
  • Liu, Yanchu
  • Weng, Chengguo

Abstract

This paper studies the optimal risk-sharing between an insurer and a reinsurer. The insurer purchases reinsurance for risk-control and decides her retention level with an objective to minimize her ruin probability. The reinsurer has control over the reinsurance price and aims to maximize her expected discounted profits up to the time when the insurer goes bankrupt. In a stochastic differential game-theoretic framework, we determine the insurer’s optimal reinsurance strategy and specify the reinsurance contract by solving a system of coupled Hamilton–Jacobi–Bellman equations. We obtain explicit solutions for the game problem when both the insurance and the reinsurance premiums are calculated according to the standard-deviation principle or the expected value principle, respectively. Our results show that, depending on the model parameters, the reinsurance contract is either provided with a peak price when the insurer has sufficient cash reserve and with a minimum price when otherwise, or is always provided with a peak price. We also perform some numerical analyses and provide economic interpretations for the results.

Suggested Citation

  • Chen, Shumin & Liu, Yanchu & Weng, Chengguo, 2019. "Dynamic risk-sharing game and reinsurance contract design," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 216-231.
    • Handle: RePEc:eee:insuma:v:86:y:2019:i:c:p:216-231
    DOI: 10.1016/j.insmatheco.2019.03.004
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    Cited by:

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    More about this item

    Keywords

    Reinsurance; Ruin probability; Nash equilibrium; Stochastic control; HJB equation;
    All these keywords.

    JEL classification:

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

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