摘要
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).
出处
《安庆师范学院学报(自然科学版)》
2008年第1期12-15,共4页
Journal of Anqing Teachers College(Natural Science Edition)
关键词
随机利率
Lundberg基本方程
标准布朗运动
泊松-几何过程
鞅方法
破产概率
random rate of intei'est
Lundberg fundamental equation
standard Brownian motion
Poisson-- Geometricprocess
martingale approach
ruin probability