稀疏风险模型的期望折扣罚金函数(英文)  

Expected discounted Penalty Function for a Thinning Risk Model

作　　者：潘洁[1,2] 王过京[2] 

机构地区：[1]安徽理工大学理学院数学系,淮南232007 [2]苏州大学数学系,苏州215006

出　　处：《应用概率统计》2009年第5期544-552,共9页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation (10571132) of China

摘　　要：本文考虑了一类风险模型, 其中保费到达过程是一个参数为λ > 0的Poisson过程, 而理赔过程是保费到达过程的稀疏过程. 在该模型下, 我们得到了期望折扣罚金函数所满足的积分方程, 积分–微分方程以及递推公式, 并且当保费和理赔额均为指数分布时, 我们使用积分–微分方程获得了破产时刻的Laplace变换和在破产时刻的赤字的闭式表达式.In this paper, we consider a risk model in which the premium arriving number process is a Poisson process with parameter λ 〉 0 while the claim number process is the thinning of the premium arriving number process. Under such a model, we obtain the integral equation, the integro-differential equation and the recursive formula for the expected discounted penalty function. Using the integro-differential equation we get the closed form expressions for the Laplace transform of the time of ruin and the deficit at ruin when the premium and the claim sizes are exponentially distributed.

关 键 词：稀疏 POISSON过程 期望折扣罚金函数 

分 类 号：O211.62[理学—概率论与数理统计]