带外生负债的保险公司最优再保险-投资策略  

Optimal Reinsurance-Investment Strategy for an Insurer with Exogenous Liability

作　　者：李婵娟[1] 李仲飞[2,3] 曾燕[2] 

机构地区：[1]中山大学数学与计算科学学院,广州510275 [2]中山大学岭南学院,广州510275 [3]中山大学管理学院,广州510275

出　　处：《中山大学学报（自然科学版）》2012年第1期1-8,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家杰出青年科学基金资助项目(70825002);国家973计划资助项目(2007CB814902);2011年度中山大学人文社会科学青年教师桐山基金资助项目;中国博士后科学基金资助项目(2011M501351)

摘　　要：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。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.

关 键 词：投资组合 再保险 资产负债管理 最大化效用 外生负债 

分 类 号：O224[理学—运筹学与控制论]