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Nonzero-Sum Stochastic Differential Reinsurance Games with Jump–Diffusion Processes

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  • Negash Medhin

    (North Carolina State University)

  • Chuan Xu

    (North Carolina State University)

Abstract

In this paper, a nonzero-sum stochastic differential reinsurance game is studied. A model including controls for the market share (advertising), investment, and reinsurance policies is considered. A jump–diffusion process is used to represent insurance claims. Necessary conditions that would lead to the Nash equilibrium can be found in the duopoly game we consider. Cases with and without controls on the reinsurance are discussed separately. Closed-form solutions for optimal strategies are derived by applying the Hamilton–Jacobi–Bellman equation. Numerical examples are given to validate the correctness of our results.

Suggested Citation

  • Negash Medhin & Chuan Xu, 2020. "Nonzero-Sum Stochastic Differential Reinsurance Games with Jump–Diffusion Processes," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 566-584, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01756-0
    DOI: 10.1007/s10957-020-01756-0
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    References listed on IDEAS

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    Cited by:

    1. Guohui Guan & Zongxia Liang & Yi Xia, 2024. "Robust mean-variance stochastic differential reinsurance and investment games under volatility risk and model uncertainty," Papers 2412.09171, arXiv.org.

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