应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2011年
3期
256-264
,共9页
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
廣義Erlang(n)分佈%破產前最大盈餘%Km分佈%積分-微分方程%閾值紅利策略
엄의Erlang(n)분포%파산전최대영여%Km분포%적분-미분방정%역치홍리책략
Generalized Erlang(n) distributed%maximum surplus before ruin%K<%m> distribu- tion%integro-differential equation%threshold dividend strategy
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K<,m>分布时的特殊情形.
本文攷慮瞭索賠時間間距為廣義Erlang(n)分佈的帶榦擾更新(Sparre Andersen)風險過程.所用的方法類似于Albrecher,et al.(2005),即將廣義Erlang(n)隨機變量分解成n箇獨立的指數隨機變量的和.建立瞭破產前最大盈餘所滿足的積分-微分方程,討論瞭索賠量分佈為K<,m>分佈時的特殊情形.
본문고필료색배시간간거위엄의Erlang(n)분포적대간우경신(Sparre Andersen)풍험과정.소용적방법유사우Albrecher,et al.(2005),즉장엄의Erlang(n)수궤변량분해성n개독립적지수수궤변량적화.건립료파산전최대영여소만족적적분-미분방정,토론료색배량분포위K<,m>분포시적특수정형.
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 vari- able 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 K<,m> distribution is considered.
