基于ARMA模型的离散时间风险过程的破产问题

Ruin problems for the discrete time risk process based on ARMA model

考虑一类具有相依结构的离散时间风险过程,其中利率和保费收入过程假设为2个不同的自回归移动平均模型.利用更新递归方法,研究了破产前最大盈余分布和索赔剩余首达某一水平的时间分布,得到了这2个重要破产量所满足的积分方程.

We consider a discrete time risk model with dependent structures,in which two different au- toregressive moving average models for the rates of interest and premiums are assumed. By using re- newal recursive technique, we study the distribution of the supremum surplus before ruin and the time that the surplus process reaches a given level for the first time, the integral equations for the two important rum quantlttes are given.