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<p>We consider an insurance market with a finite or infinite number of competitive insurers. Each insurer makes an optimal decision on reinsurance and investment to maximize her expected utility function that depends on her individual wealth as well as the average wealth of her competitors. This decision-making problem incorporating relative performance concerns is modeled as an <i>n</i>-player game and as a mean-field game (MFG) in the case of infinite insurers. We obtain the explicit optimal reinsurance-investment strategy when a Nash equilibrium is reached. The impacts of relative performance concerns on the optimal reinsurance-investment decisions are examined both theoretically and numerically.</p>

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Equilibrium reinsurance and investment strategies in N-insurer and MFGs

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Guanxia Zhu,
  • Chen Zhang

摘要

We consider an insurance market with a finite or infinite number of competitive insurers. Each insurer makes an optimal decision on reinsurance and investment to maximize her expected utility function that depends on her individual wealth as well as the average wealth of her competitors. This decision-making problem incorporating relative performance concerns is modeled as an n-player game and as a mean-field game (MFG) in the case of infinite insurers. We obtain the explicit optimal reinsurance-investment strategy when a Nash equilibrium is reached. The impacts of relative performance concerns on the optimal reinsurance-investment decisions are examined both theoretically and numerically.