Optimal Reinsurance Contracts with Ambiguity Aversion and Continuous Dividends under the Principal-Agent Framework

本文研究了带有连续分红的保险公司和再保险公司，在委托代理框架下基于 Stackelberg 随机 微分博弈的最优再保险-投资问题。保险公司通过购买比例再保险来转移风险，且根据期望值保 费原则支付再保险的保费。保险公司和再保险公司的博弈过程符合 Stackelberg 随机微分博弈， 在均方差准则下建立保险公司和再保险公司的目标函数，利用动态规划原理，通过求解相应的 Hamilton-Jacobi-Bellman (HJB) 方程得出保险公司和再保险公司的纳什均衡策略的显示表达 式。最后，利用数据分析及 MCMC 方法估计模型中的主要参数。This paper studies the optimal reinsurance-investment problem of an insurance com- pany and a reinsurer with continuous dividends under the principal-agent framework, based on the Stackelberg stochastic differential game. The insurance company trans- fers risks by purchasing proportional reinsurance and pays the reinsurance premium according to the expected value premium principle. The game process between the insurance company and the reinsurer conforms to the Stackelberg stochastic differen- tial game. Under the mean-variance criterion, the objective functions of the insurance company and the reinsurer are established. By using the principle of dynamic pro- gramming and solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, the explicit expressions of the Nash equilibrium strategies of the insurance company and the reinsurer are derived. Finally, data analysis and the Markov Chain Monte Carlo (MCMC) method are used to estimate the main parameters in the model.