随机保费模型下绝对破产概率的可微性以及渐近性（英文）  

Differentiability and Asymptotic Properties of Gerber-Shiu Function Associated with Absolute Ruin Time for a Risk Model with Random Premium Income

作　　者：徐林[1] 章礼明[1] 吴丽媛[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,芜湖241003

出　　处：《应用概率统计》2015年第3期277-288,共12页Chinese Journal of Applied Probability and Statistics

基　　金：supported by National Natural Science Foundation of China(11201006);Natural Science Foundation of Anhui Province(1508085MA11,1408085MA07)

摘　　要：本文研究了具有随机保费收入的风险模型的Gerber-Shiu罚金函数的可微性以及渐近性质,随机保费收入通过一个复合泊松过程刻画.本文得到了Gerber-Shiu函数所满足的积分微分方程,给出了Gerber-Shiu罚金函数二次可微与三次可微的充分条件.当所讨论的罚金函数是三次可微的时候,前述积分微分方程可以转化为一般的常微分方程.利用常微分方程的标准方法,当个体随机保费和随机理赔都是指数分布的时候,得到了绝对破产概率在初始盈余趋向于无穷大时的渐近性质.In this paper, the differentiability and asymptotic properties of Gerber-Shiu expected discounted penalty function （Gerber-Shiu function for short） associated with the absolute ruin time are investigated, where the risk model is given by classical risk model with additional random premium incomes. The additional random premium income process is specified by a compound Poisson process. A couple of integro-differential equations satisfied by Gerber-Shiu function are derived, several sufficient conditions which guarantee the second-order or third-order differentiability of Gerber-Shiu function are provided. Based on the differentiability results, when the individual claim and premium income are both exponential distribution, the previous integro-differential equations can be deduced into a third-order constant ordinary differential equation （ODE for short）. With the standard techniques on ODE, we find the asymptotic behavior of absolute ruin probability when the initial surplus tends to infinity.

关 键 词：绝对破产时间 Gerber-Shiu罚金函数 随机保费 可微性 渐近性质 

分 类 号：O212.3[理学—概率论与数理统计]