离散的相依风险模型的破产问题

Ruin Problems for Correlated Discrete Risk Model

研究一类索赔时间相依的离散风险模型,模型中假设每次主索赔可能引起一次副索赔,而每次副索赔有可能延迟发生.通过引入辅助模型,运用概率论的分析方法得到了破产前瞬时盈余和破产时赤字联合分布的递推解,以及初始值为0时最终破产概率的明确表达式.最后结合保险实例进行了数值模拟.

Considering a discrete risk model with time-correlated claims,in which every main claim may produce a by-claim and the occurrence of the by-claim may be delayed. By means of auxiliary model,using the methods of probability,we obtain the recursive formula of the joint distribution of the surplus immediately before ruin and deficit at ruin. Furthermore,the explicit expression for the probability is given when the initial surplus is zero.Finally,we show some numerical results according to the insurance case.