带外生负债的保险公司最优再保险-投资策略

研究了外生负债影响下保险公司的最优再保险-投资策略,其中假设保险公司的目标是最大化终端财富的期望指数效用;盈余过程服从扩散模型;风险资产和负债均由几何布朗运动刻画。运用随机动态规划方法,得到了保险公司在(i)进行投资且允许购买比例再保险或获取新业务,(ii)进行投资但只允许购买比例再保险,不能获取新业务,两种情形下的最优再保险-投资策略以及最优值函数的解析式。最后,采用数值算例阐述了外生负债与市场参数对最优策略的影响。

Optimal Reinsurance-Investment Strategy for an Insurer with Exogenous Liability

The optimal reinsurance-investment strategy for an insurer with an exogenous liability is considered.Assume that the aim of the insurer is to maximize the expected exponential utility of the terminal wealth;the surplus process of the insurer follows a diffusion model while the risky assets’ prices and the exogenous liability are governed by geometric Brownian motions.By employing the stochastic dynamic programming,the closed form of the optimal reinsurance-investment strategy and the optimal value function are derived under two cases:(i) the insurer can invest in a financial market and purchase proportional reinsurance or acquire new business,(ii) the insurer can invest in a financial market and purchase proportional reinsurance,but not acquire new business.Finally,a numerical example is given to show the impact of the exogenous liability and the market parameters on the optimal strategy.