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Reinsurance–investment game between two α-maxmin mean–variance insurers

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  • Qian Zhang
  • Guoyong Zhou
  • Jing Fu

Abstract

This paper examines a non-zero-sum stochastic differential reinsurance-investment game between two competitive insurers under the α-maximin mean-variance criterion. Both insurers can purchase proportional reinsurance and invest in a financial market consisting of one risk-free asset and one risky asset, and each insurer is concerned with its terminal surplus and relative performance compared to its competitor. The insurers aim to maximize the α-maximin mean-variance utility, which allows them to exhibit different attitudes towards model ambiguity. By solving the extended Hamilton-Jacobi-Bellman (HJB) equations for both insurers, we derive the α-robust equilibrium reinsurance and investment strategies. Finally, several numerical examples are provided to illustrate the impact of some model parameters on the equilibrium strategies.

Suggested Citation

  • Qian Zhang & Guoyong Zhou & Jing Fu, 2025. "Reinsurance–investment game between two α-maxmin mean–variance insurers," PLOS ONE, Public Library of Science, vol. 20(6), pages 1-16, June.
    • Handle: RePEc:plo:pone00:0326125
    DOI: 10.1371/journal.pone.0326125
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