具有风险相依的主从再保险和投资博弈

Stackelberg Reinsurance and Investment Game with Risk Dependence

摘要: 本文在期望效用最大准则下研究保险公司与再保险公司间最优的主从再保险和投资博弈问题。假设保险公司从事两类具有共同冲击相依的保险业务，再保险公司既从事再保险业务也从事保险业务。再保险双方均投资于无风险资产和股票。其中，股票价格由Ornstein-Uhlenbeck (O-U)过程来描述。利用动态规划原理，分别推导出再保险双方的最优再保险合同和投资策略以及对应的值函数。最后，通过数值分析分析了模型参数对最优策略的影响。

Abstract: This paper investigates the optimal Stackelberg reinsurance and investment game between an insurer and a reinsurer under the expected utility maximization criterion. It is assumed that the insurer operates two classes of insurance businesses with common shock dependence, while the reinsurer engages in both reinsurance and direct insurance businesses. Both parties allocate their capital to risk-free assets and stocks, where the stock price dynamics are characterized by the Ornstein-Uhlenbeck (O-U) process. By using the dynamic programming principle, the optimal reinsurance contracts, investment strategies, and corresponding value functions for both the insurer and reinsurer are derived separately. Finally, numerical analyses are conducted to illustrate the impact of model parameters on the optimal strategies.