两类索赔相关风险模型的罚金折现期望函数  

On 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]中国人民解放军理工大学理学院,江苏南京211101 [2]西北工业大学应用数学系,陕西西安710072

出　　处：《高校应用数学学报（A辑）》2009年第2期137-145,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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模型.两类索赔计数过程分别为独立的广义Poisson过程和广义Erlang(2)过程.得到了该风险模型的罚金折现期望函数满足的积分微分方程及该函数的Laplace变换的表达式,且当索赔额均服从指数分布时,给出了罚金折现期望函数及破产概率的明确表达式.In this paper two-correlated claims model is considered. Claim occurrence of both classes relates to the generalized Poisson and generalized Erlang（2） processes. Integro-differential equations satisfied by the expected discounted penalty functions are derived. Laplace transforms of the expected discounted penalty functions are obtained. Explicit results of the expected discounted penalty functions and ruin probability are derived when the claims from both classes are exponentially distributed.

关 键 词：广义Poisson过程 广义Erlang(2)过程 罚金折现期望函数 破产概率 LAPLACE变换 

分 类 号：O211.9[理学—概率论与数理统计]