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Multiple per-claim reinsurance based on maximizing the Lundberg exponent

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  • Meng, Hui
  • Wei, Li
  • Zhou, Ming

Abstract

In this paper, we consider the optimal per-claim reinsurance problem for an insurer who designs a reinsurance contract with multiple reinsurance participants. In contrast to using the value-at-risk as a short-term risk measure, we take the Lundberg exponent in risk theory as a risk measure for the insurer over a long-term horizon because the Lundberg upper bound performs better in measuring the infinite-time ruin probability. To reflect various risk preferences of the reinsurance participants, we adopt a type of combined premium principle in which the expected premium principle, variance premium principle, and exponential premium principle are all special cases. Based on maximization of the insurer's Lundberg exponent, the optimal reinsurance is formulated within a static setting, and we derive optimal multiple reinsurance strategies within a general admissible policies set. In general, these optimal strategies are shown to have non-piecewise linear structures, differing from conventional reinsurance strategies such as quota-share, excess-of-loss, or linear layer reinsurance arrangements. In some special cases, the optimal reinsurance strategies reduce to classical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:112:y:2023:i:c:p:33-47
    DOI: 10.1016/j.insmatheco.2023.05.009
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    1. Yuta Otsuki & Shotaro Yagishita, 2024. "Optimal reinsurance and investment via stochastic projected gradient method based on Malliavin calculus," Papers 2411.05417, arXiv.org.

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    More about this item

    Keywords

    Bisection method; Combined premium principle; Lundberg exponent; Multiple reinsurance; Per-claim reinsurance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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