竞争性保险公司最优投资与风险控制的平均场博弈方法
A Mean Field Game Approach to Optimal Investment and Risk Control for Competitive Insurers
摘要: 本文对一个由多家竞争性保险公司构成的保险市场中的最优投资问题进行了分析. 在该市场中, 保 险公司在相对财富指数效用准则下, 各保险公司通过终端时刻平均财富相互影响. 保险公司通过控 制保单规模(即持有的保单数量)来管理其风险敞口. 每家保险公司将其资本配置于无风险债券和受 共同噪声影响的风险资产, 其索赔风险则通过泊松跳跃－扩散过程进行建模. 随着保险公司数量趋 近于无穷, 我们推导出了平均场博弈平均场均衡. 基于此解, 我们为有限市场主体情形构建了一个 近似纳什均衡. 为验证理论结果, 我们对竞争强度、风险容忍度水平以及索赔发生频率等模型关键 参数进行了敏感性分析.
Abstract: We analyze an optimal investment and risk control problem in an insurance mar- ket comprising multiple competitive insurers interacting through mean-field dynamics governed by terminal wealth under exponential utility with relative performance con- siderations. The insurers manage their risk exposure by controlling the number of policy. Each insurer allocates capital between a risk-free bond and a risky asset sub- ject to common noise, while its claims risk is modeled by a Poisson jump-diffusion process. We derive the stationary mean-field equilibrium strategy for the mean field game as the number of insurers approaches infinity. Building upon this solution, we construct an approximate Nash equilibrium for the finite-population case. We con- duct numerical simulations to assess the equilibrium’s sensitivity to key parameters, including the intensity of competition, the level of risk tolerance, and the claim arrival.
文章引用：樊菁婧, 王世花. 竞争性保险公司最优投资与风险控制的平均场博弈方法[J]. 应用数学进展, 2026, 15(3): 441-462. https://doi.org/10.12677/AAM.2026.153118

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