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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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    References listed on IDEAS

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    1. Zhang, Xin & Meng, Hui & Zeng, Yan, 2016. "Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 125-132.
    2. Xia Han & Zhibin Liang & Virginia R. Young, 2020. "Optimal reinsurance to minimize the probability of drawdown under the mean-variance premium principle," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(10), pages 879-903, November.
    3. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    4. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.
    5. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
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