保险公司最优有界分红和融资控制策略

Optimal Bounded Dividend Distribution and Capital Injection Control Strategies of Insurance Company

文章研究了保险公司的最优分红策略问题,主要通过比例再保险策略、有界分红策略和融资策略来控制公司盈余过程,以达到降低公司风险和使得期望折现效益最大化的目的.首先给出一个随机控制问题,用漂移Brown运动描述公司的盈余过程,把公司破产前最大化分红现值的期望值与融资现值的期望值之差设定为优化目标.然后通过随机控制定理得到相应的HJB方程.最后解出相应方程的解并证明这个解与最优的值函数相等,在求解的过程中找出了最优的分红和再保险策略,并且给出了值函数以及最优策略的解析表达式.

The paper studies the optimal control problem of an insurance company by choosing a risk policy, a dividend distribution strategy and a capital injection policy to reduce risk and maximize the total discounted expected utility of consumption. The dividend payout rate is bounded. At first, it gives a stochastic control problem and describes the surplus process of corporation via a Brownian motion. The ultimate objective is to maximize the expected discounted dividend payments minus the expected discounted costs of capital injection before the company goes bankrupt. Then, it finds the HJB equation corresponding to the above stochastic control problem by using the stochastic control theory. Based on this equation, the paper derives the solution to it and then proves that the solution is the value function. Meanwhile, optimal control strategies are expressed. Moreover, it derives a closed form solution and the optimal strategies.