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

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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.

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Authors and Affiliations

  1. North Carolina State University, Raleigh, NC, USA

    Negash Medhin & Chuan Xu

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  1. Negash Medhin
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  2. Chuan Xu
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Correspondence to Negash Medhin.

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Communicated by Boris S. Mordukhovich.

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Medhin, N., Xu, C. Nonzero-Sum Stochastic Differential Reinsurance Games with Jump–Diffusion Processes. J Optim Theory Appl 187, 566–584 (2020). https://doi.org/10.1007/s10957-020-01756-0

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