$n$类相依保险业务下的最优再保险和投资

本文研究了一个保险公司经营$n$类相依保险业务下,最优时间一致的再保险和投资问题．为了减少理赔风险,保险公司可以购买再保险;为了增加财富保险公司可以在金融市场上投资．金融市场由一个无风险资产和$n$个相依的风险资产组成,风险资产的价格满足扩散过程．然后,利用随机分析理论,我们建立了保险公司的财富过程．我们的主要目标是,寻找最优时间一致的再保险和投资策略最大化终值财富的均值同时最小化终值财富的方差．通过使用随机控制和随机动态规划技术,我们建立了推广的Hamilton-Jacob-Bellman (HJB)方程．进而,通过求解推广的HJB方程,我们得到了最优时间一致的再保险和投资策略以及相应值函数的显式解．最终,通过数值实验解释了模型参数对最优时间一致的再保险和投资策略的影响．

Optimal Reinsurance and Investment under $n$ Dependent Insurance Businesses

This paper investigates an optimal time-consistent reinsurance and investment problem with $n$ dependent insurance businesses for an insurance company. The insurance company is allowed to purchase reinsurance for reducing claim risk and invest in the financial market for increasing wealth. The financial market consists of one risk-free asset and $n$ correlated risky assets, whose price processes are described by diffusion processes. Then, we establish the wealth process of the insurance company by using the stochastic analysis theory. Our main goal is to find an optimal time-consistent reinsurance and investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. By applying the stochastic control and stochastic dynamic programming techniques, we establish the extended Hamilton-Jacob-Bellman (HJB) equation. Explicit solutions for the optimal reinsurance and investment strategy as well as the corresponding value function are obtained by solving the extended HJB equation. Finally, numerical experiments illustrate the effects of model parameters on the optimal time-consistent reinsurance and investment strategy.