风险模型的破产概率的计算及其相关问题

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。

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

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.