带红利的两类索赔风险模型的Gerber-Shiu函数  

On the Gerber-Shiu Functions for a Risk Model with Dividends Involving Two Classes of Insurance Risks

作　　者：范庆祝[1,2] 尹传存[2] 

机构地区：[1]石河子大学商学院商务信息系,新疆五家渠831300 [2]曲阜师范大学数学科学学院,曲阜273165

出　　处：《工程数学学报》2009年第1期51-59,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10471076;10771119);山东省自然科学基金(Y2004A06);教育部科技重点项目(206091)

摘　　要：本文考虑了一类具有常数红利界限的包含两个独立险种风险模型的Gerber-Shiu罚金折现期望函数,我们假设两个索赔次数过程是独立的Poisson过程和广义Erlang(2)过程。得到了关于Gerber-Shiu罚金折现期望函数满足的积分-微分方程及其边界条件。特别,当这两类索赔额服从同一指数分布时,给出了Gerber-Shiu罚金折现期望函数的精确解。最后给出了一个例子。In this paper, we consider the Gerber-Shiu expected discounted penalty functions for a risk model involving two independent classes of insurance risks with a dividend barrier. We assume that the two claim number processes are independent Poisson and generalized Erlang （2） processes, respectively. Integro-differential equations with boundary conditions for the Gerber-Shiu discounted penalty functions are derived. In particular, explicit results are derived when the claims from both classes have the same exponential distribution. Finally, an example is given.

关 键 词：双险种风险模型 红利 复合POISSON过程 Gerber-Shiu罚金折现期望函数 积分-微分方程 

分 类 号：O211.9[理学—概率论与数理统计]