具有两种副索赔的离散相依风险模型破产问题

考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,分别得出了该风险模型初始盈余为0时破产前盈余与破产时赤字的联合分布的表达式、初始盈余为u时破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时的破产概率,以及初始盈余为u时的破产概率求解方法.最后,结合实例进行了数值模拟.

The Ruin Problems of Correlated Discrete Risk Model with Two Kinds of Deputy Claims

The correlated discrete risk model with two kinds of deputy claims was considered. Every main claim may produce two kinds of deputy claim, and the occurrence of the first kind of deputy claim may be delayed. By means of auxiliary model, the expression of the joint distribution of the surplus immediately before ruin and deficit at ruin was obtained when the initial surplus is zero, the recursive formula of the joint distribution of the surplus immediately before ruin and deficit at ruin was obtained when the initial surplus is u, the expression for the ruin probability was obtained when the initial surplus is zero, and the solution for the ruin probability was obtained when the initial surplus is u. Finally, some numerical results according to the insurance case were showed.