多智能体再保险链中的均衡分析
Equilibrium analysis in a multi-agent reinsurance chain
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中文总结 AI 辅助
研究多层再保险链中保险公司与再保险公司互动，用斯塔克尔伯格微分博弈等方法，结合动态规划与博弈论，在均值-方差准则下求解均衡策略，通过数值分析发现保险市场竞争加剧使再保险链各层合同安全负荷降低。
中文摘要 AI 辅助
本文在随机微分博弈框架下研究了一个包含m个竞争保险公司和n个再保险公司的多层再保险链。具体而言，采用斯塔克尔伯格微分博弈来刻画链中各层再保险买卖双方的战略互动。此外，建立了一个非零和博弈模型来捕捉保险公司之间的竞争行为。保险公司和再保险公司都被允许投资无风险资产和风险资产。为检验不同合同类型下再保险链的异质性，分别对比例再保险和超额损失再保险进行了分析。通过结合动态规划和博弈论，在均值-方差（MV）准则下求解扩展的汉密尔顿-雅可比-贝尔曼（HJB）系统，得出了投资和再保险的闭式均衡策略。进行了数值分析以探究关键参数对均衡策略的影响。结果表明，保险市场竞争加剧会导致再保险链各层再保险合同的安全负荷降低。
英文摘要
This paper investigates a multi-layer reinsurance chain within a stochastic differential game framework involving m competing insurers and n reinsurers. Specifically, Stackelberg differential games are employed to characterize the strategic interactions between reinsurance buyers and sellers at each layer of the chain. In addition, a non-zero-sum game model is established to capture the competitive behavior among insurers. Both insurers and reinsurers are allowed to invest in a risk-free asset and a risky asset. To examine the heterogeneity of reinsurance chains under different contract types, the analysis is conducted separately for proportional reinsurance and excess-of-loss reinsurance. By combining dynamic programming and game theory, closed-form equilibrium strategies for investment and reinsurance are derived by solving the extended Hamilton-Jacobi-Bellman (HJB) systems under the mean-variance (MV) criterion. Numerical analysis is conducted to explore the impact of key parameters on the equilibrium strategies. The results indicate that intensified competition in the insurance market leads to a reduction in the safety loadings of reinsurance contracts at each layer of the reinsurance chain.
