具有一阶自回归结构的离散时间再保险模型的破产概率

Ruin probability under discrete time reinsurance model with autoregressive structure of order one structure

考虑一类离散时间再保险模型,在模型中假定索赔间隔时间、索赔额以及利息率为3个具有不同参数的一阶自回归结构,得到了一般再保险形式下破产概率满足的积分方程.作为应用,得到了比例再保险和超额损失再保险下破产概率的递归方程.最后,利用递归更新方法得到比例再保险情况下破产概率的上界估计.

Considering a class of discrete time reinsurance model,in which the occurrence time of the claims,the claim payment and the rates of interest are assumed to be AR（1）structure with different parameter.For this general model,the integral equation for ruin probability is derived.As applications,the integral equations for ruin probabilities of the proportional reinsurance and the excess of loss reinsurance are obtained.Finally,the upper bound of the ruin probability for proportional reinsurance is derived by using renewal recursive technique.