经典风险模型下带有随机利率的一类破产问题

A ruin problem about classical risk process underrandom interest force

考虑利率随机性通过标准布朗运动和普哇松过程来描述情形下的一类破产问题.利用鞅方法,得到了此情形下经典风险模型的Lundberg基本方程,并考虑了其解的两个有效应用,从而得到了破产概率、盈余首次到达某给定水平x(x>u)的概率、f(x,y0)及初始盈余u=0情况下破产时单位赔付现值的表达式.最后给出了当个体理赔服从指数分布情形下的一些结果.

The interest force accumulated process is modeled by standard Brownian motion and Poisson process in this article. By martingale approach, Lundberg＇s fundamental equation is got and two effective applications of its solutions are considered. Hence some results about the probability of ruin, the probability that the surplus reaches the given level x（x〉u） and f（x,y｜0）,are obtained. The results here are a generalization of Gerber and Shiu（1998） under constant interest force. Finally,some results are obtained when the individual claim amount obeys the exponential distribution with parameter α.