风险模型的破产概率的计算及其相关问题  

The Ruin Probability of Erlang(n) Risk Process and Related Problems

作　　者：郑芸[1] 吴黎军[1] 

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《塔里木大学学报》2007年第2期25-28,共4页Journal of Tarim University

摘　　要：本文主要研究了在Sparre Andersen风险过程中时间间隔过程为Erlang(n)的破产概率及其相关问题。在此基础上,特别考虑了理赔量为possion理赔过程时候满足的破产概率的显示表达形式,同时计算出了最大盈余量未到达b时的带有边际条件的同类积分—微分方程破产概率的表达形式方程的通解问题和当n=2时的生存概率的显示表达形式。It was studied that the distribution of ruin probability in Sparre Andersen risk process with the inter - claim times being Erlang （n） distribution. Meanwhile, It was analyzed that the distribution of ruin probability that the surplus process attained a given level from the initial surplus without first falling below zero. The probability, viewed as a function of the initial surplus and the given level, satisfied a homogeneous integro - differential equation with certain boundary conditions. Its solution could be expressed as a linear combination of linearly independent particular solutions of homogeneous integro - differential equation. Explicit results were obtained when the individual claim amounts were rationally distribution. When n = 2, all the results could be expressed explicitly in terms of the non - ruin probability.

关 键 词：SPARRE ANDERSEN风险模型 Erlang(n)时间间隔过程 破产概率 

分 类 号：O212.7[理学—概率论与数理统计]