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Optimal reinsurance policies with two reinsurers in continuous time

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  • Meng, Hui
  • Zhou, Ming
  • Siu, Tak Kuen

Abstract

An optimal reinsurance problem of an insurer is studied in a continuous-time model, where insurance risk is partly transferred to two reinsurers, one adopting the expected-value premium principle and another one using the variance premium principle. The insurer aims to select an optimal reinsurance arrangement to minimize the probability of ruin. To provide an easy-to-implement solution to the problem, (semi)-explicit expressions for the optimal reinsurance strategies as well as the minimal ruin probabilities are derived for several claims distributions. Numerical studies including a real-data example based on the Danish fire insurance losses are provided to illustrate the solution of the problem. Our empirical results based on the Danish data reveal that the heavy-right-tailedness of claims distributions has a significant impact on the optimal reinsurance strategies and has a quite pronounced impact on the residual risk described by the minimal ruin probability.

Suggested Citation

  • Meng, Hui & Zhou, Ming & Siu, Tak Kuen, 2016. "Optimal reinsurance policies with two reinsurers in continuous time," Economic Modelling, Elsevier, vol. 59(C), pages 182-195.
    • Handle: RePEc:eee:ecmode:v:59:y:2016:i:c:p:182-195
    DOI: 10.1016/j.econmod.2016.07.009
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    References listed on IDEAS

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    Cited by:

    1. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    2. Feng, Yang & Siu, Tak Kuen & Zhu, Jinxia, 2024. "Optimal payout strategies when Bruno de Finetti meets model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 148-164.
    3. Meng, Hui & Liao, Pu & Siu, Tak Kuen, 2019. "Continuous-time optimal reinsurance strategy with nontrivial curved structures," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    4. Liyuan Lin & Fangda Liu & Jingzhen Liu abd Luyang Yu, 2023. "The optimal reinsurance strategy with price-competition between two reinsurers," Papers 2305.00509, arXiv.org.
    5. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2023. "Reinsurance games with two reinsurers: Tree versus chain," European Journal of Operational Research, Elsevier, vol. 310(2), pages 928-941.
    6. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.

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