一类带利率的马氏风险模型  

A Kind of Markovian Risk Model with Interest Rate

作　　者：夏征[1] 王春伟[1] 杨万才[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《河南科技大学学报（自然科学版）》2011年第6期72-76,9,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省基础与前沿技术研究计划项目(092300410178);河南科技大学博士科研启动基金项目(09001443)

摘　　要：考虑了带有常利率的马氏相依风险模型,保险公司的经营受到外部马氏环境的干扰更符合保险公司的实际经营状况。利用盈余过程的马氏性及随机微分方程得到了该模型期望折现罚金函数(Gerber-Sh iu函数)所满足的积分微分方程及边值条件,并运用Lap lace变换得到了外部环境只有两个状态并且索赔额服从指数分布时Gerber-Sh iu函数满足的积分方程。This paper considers a Markov-dependent risk model with constant interest force,which accords with actual operating condition.By using Markov property of the surplus process and the theory of stochastic differential equation,the integro-differential equations satisfied by the expected discounted penalty function（also named Gerber-Shiu function） and the boundary conditions are obtained.When the claims obey exponential distribution and the state of the external Markovian environment is two-state,the integral equations satisfied by the Gerber-Shiu function are obtained.

关 键 词：GERBER-SHIU函数 马尔科夫过程 积分微分方程 破产概率 

分 类 号：O211.6[理学—概率论与数理统计]