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Stochastic Pareto-optimal reinsurance policies

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  • Zeng, Xudong
  • Luo, Shangzhen

Abstract

We model reinsurance as a stochastic cooperation game in a continuous-time framework. Employing stochastic control theory and dynamic programming techniques, we study Pareto-optimal solutions to the game and derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation. After analyzing the HJB equation, we show that the Pareto-optimal policies may be classified into either unlimited excess of loss functions or proportional functions based on different premium share principles. To illustrate our results, we solve several examples for explicit solutions.

Suggested Citation

  • Zeng, Xudong & Luo, Shangzhen, 2013. "Stochastic Pareto-optimal reinsurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 671-677.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:671-677
    DOI: 10.1016/j.insmatheco.2013.09.006
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    References listed on IDEAS

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    1. Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1996. "Stochastic Cooperative Games in Insurance and Reinsurance," Other publications TiSEM f2cd7428-cd39-4462-af76-2, Tilburg University, School of Economics and Management.
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    8. Luo, Shangzhen & Taksar, Michael & Tsoi, Allanus, 2008. "On reinsurance and investment for large insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 434-444, February.
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    Cited by:

    1. Danping Li & Dongchen Li & Virginia R. Young, 2017. "Optimality of Excess-Loss Reinsurance under a Mean-Variance Criterion," Papers 1703.01984, arXiv.org, revised Mar 2017.
    2. Li, Danping & Li, Dongchen & Young, Virginia R., 2017. "Optimality of excess-loss reinsurance under a mean–variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 82-89.
    3. 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.
    4. 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.

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