具有两类索赔相关风险过程的罚金折现函数  

The Expected Discounted Penalty Functions for Two Correlated Aggregate Claims Model

作　　者：张燕[1,2] 田铮[2] 刘向增[2] 

机构地区：[1]解放军理工大学理学院,南京211101 [2]西北工业大学数学系,西安710072

出　　处：《数学的实践与认识》2008年第23期12-20,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(60375003);国家航空基金(03I53059)

摘　　要：考虑两类索赔相关风险过程.两类索赔计数过程分别为独立的Poisson和广义Erlang(2)过程.将该过程转换为两类独立索赔风险过程,得到了该过程的罚金折现函数满足的积分微分方程及该函数的拉普拉斯变换的表达式,且当索赔额服从指数分布时,给出了罚金折现函数及破产概率的表达式.We consider a risk model with two dependent classes of insurance husiness. In this model the two claim number processes are correlated. Claim occurrence of both classes relate to generalized Poisson and generalized Erlang（2） processes. Firstly, integro differential equations satisfied by the expected discounted penalty functions are derived by changing the model into two independent model. Laplace transforms of the expected discounted penalty functions are obtained. Secondly, explicit expressions for the expected discounted penalty functions and ruin probability are obtained when the claims from both classes are exponentially distributed.

关 键 词：POISSON过程 广义Erlang(2)过程 罚金折现函数 破产概率 拉普拉斯变换 

分 类 号：F840[经济管理—保险] F224