带干扰广义Elang(n)风险过程的破产前最大盈余(英文)  

The Maximum Surplus before Ruin in a Generalized Erlang(n) Risk Process Perturbed by Diffusion

作　　者：江五元[1] 刘再明[2] 

机构地区：[1]湖南理工学院数学学院,岳阳414006 [2]中南大学数学学院,长沙410075

出　　处：《应用概率统计》2011年第3期256-264,共9页Chinese Journal of Applied Probability and Statistics

基　　金：Supported by the Research Foundation of Education Bureau of Hunan Province (10C0754)

摘　　要：本文考虑了索赔时间间距为广义Erlang(n)分布的带干扰更新(Sparre Andersen)风险过程. 所用的方法类似于Albrecher, et al.(2005), 即将广义Erlang(n)随机变量分解成n个独立的指数随机变量的和. 建立了破产前最大盈余所满足的积分-微分方程, 讨论了索赔量分布为Km分布时的特殊情形.In this paper,we discuss a renewal risk process（Sparre Andersen risk model） perturbed by diffusion in which the claim inter-arrival times are generalized Erlang（n） distributed.The approach used is similar to that of Albrecher,et al.（2005）,decomposing a generalized Erlang（n） random variable into an independent sum of n exponential random variables.Integro-differential equations with certain boundary conditions for the distribution of the maximum surplus before ruin are obtained.The special case where the claim size distribution is a Km distribution is considered.

关 键 词：广义Erlang(n)分布 破产前最大盈余 Km分布 积分-微分方程 阈值红利策略 

分 类 号：O211.6[理学—概率论与数理统计]