带有随机利率的复合Poisson-Geometric过程的破产问题

A Ruin Problem about Compound Poisson-Geometric Processunder Random Interest Rate

考虑利率的随机性,通过标准布朗运动和泊松-几何过程来描述一类破产问题,利用鞅方法,得到了Lund-berg基本方程,并给出了其解的两个有效应用,从而得到了破产概率Ψ(u)和盈余首次到达某给定水平x(x>u)概率Ψx(u)的一般表达式。最后给出了当个体理赔服从参数α为指数分布的Lundberg基本方程的两个具体解,由此可以进一步得到破产概率Ψ(u)和盈余首次到达某给定水平x(x>u)概率Ψx(u)的具体表达式。

Considering the random of interest rate, we describe one calss of ruin problem by standard Brownian mo tion and Poisson--Geometric process. By martingale approach, Lundbery＇s fundamental equation is gotten and two effective applications of its solutions are presented. Then the results are obtained that the expressions of ruin probability ψ（u） and the probability ψ（u） of the surplus reach the given lexel x（x〉u）. Finally, the solutions of Lundberg function are given when the individual claim amount obeying the exponential distribution with the parameter a. By the theories of the paper ,we can further get the concrete expressions of ruin probabilityand ψ（u） the probability ψ（u） of the surplus reaching the given lexel x（x〉u）.