两个风险模型的破产概率的比较

经典风险模型中,保费收入是时间的线性函数。一种推广的风险模型是用泊松过程取代时间的线性函数来描述保费收入过程,并给出了这两个风险模型下各自的破产概率所满足的积分方程。基于后一种风险模型,在一个无穷小的时间区间内,根据理赔的次数和收取保单的次数,应用全概率公式,得出了相应的积分方程。

A comparison between two ruin probabilities in two risk models

In the classical risk model,the income of insurance premiums is a linear function of time. Among the generalization risk models,one is to replace the linear function of time by Poisson process in describing the income process of insurance premiums.In this paper the integral equations of ruin probabilities are given respectively in the two risk models. Based on the total probability formula,the integral equation of ruin probability in the second risk model is deduced in a infinitesimal time interval according to the numbers of sold insurance and claim.