一类二维风险模型的破产概率

The Ruin Probability of a Two-dimensional Risk Model

本文讨论了含正、负风险的和二维风险模型的破产概率问题.定义了三种不同的破产概率,并运用一维风险过程的结果得到这些破产概率的简单边界.引进参数a=(a1,a2),利用鞅方法讨论破产概率Ψa(a1u1+a2u2),得到一个关于生存概率Φa(a1u1+a2u2)的积分-微分方程.

We consider a bivariate risk model with positive and negative risk sums. Three different types of ruin probabilities are defined. Using some results of one - dimensional risk process, simple bounds for the two -dimensional ruin probabilities are obtained. Introduce the parameter a（ a1, a2 ）, use the martingale method to discuss the ruin probability ψa（a1u1＋a2u2）. We derive the integral- differential equation for the ruin probability Фa（a1u1＋a2u2）