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

Negash Medhin () and Chuan Xu ()
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Negash Medhin: North Carolina State University
Chuan Xu: North Carolina State University

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 14, 566-584

Abstract: 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.

Keywords: Hamilton–Jacobi–Bellman equation; Stochastic differential game; Nonzero-sum reinsurance game; Jump–diffusion process; 49L20; 91A15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01756-0

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