Threshold分红策略下带干扰的两类索赔风险模型的Geber-Shiu函数(英文)  

The Gerber-Shiu Penalty Functions for a Perturbed Risk Model with Two Classes of Risks and a Threshold Dividend Strategy

作　　者：孙国红[1] 张春生[1] 季兰朋[2,3] 

机构地区：[1]天津农学院基础科学系,天津300384 [2]南开大学数学学院,天津300071 [3]瑞士洛桑大学精算系,洛桑1015

出　　处：《应用概率统计》2011年第5期543-560,共18页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the Tianjin Natural Science Foundation(08JCYBJC02200);the Keygrant Project of Chinese Ministry of Education(309009);the Natural Science Foundation of China(11171164)

摘　　要：本文研究了在threshold分红策略下带干扰的两类索赔风险模型的Geber-Shiu函数.这里假设两个索赔计数过程为独立的更新过程,其中一个为Poisson过程另一个为时间间隔服从广义Erlang(2)分布的更新过程.本文得到了threshold分红策略下Gerber-Shiu函数所满足的积分-微分方程及其边界条件.最后,本文指出threshold分红策略下Gerber-Shiu函数可以由不分红(即:6=∞)时所对应的Geber-Shiu函数和一个齐次积分-微分方程的线性独立解表示出来.In this paper, we study the perturbed risk model with two classes of claims and a threshold dividend strategy. We assume that the two claim counting processes are, respectively, Poisson and renewal process with generalized Erlang（2） inter-claim times. Integro-differential equations and certain boundary conditions satisfied by the Gerber-Shiu penalty functions are derived in terms of matrices. Finally, we show that the closed form for the Gerber-Shiu penalty functions can be expressed by the Gerber-Shiu penalty functions without dividend payments and the matrix composed of two linearly independent solutions to the corresponding homogeneous integro-differential equations.

关 键 词：两类索赔 Geber-Shiu函数 threshold分红策略 积分-微分方程 

分 类 号：O211.67[理学—概率论与数理统计]