具有延迟索赔的离散时间更新风险模型的有限时间生存概率

经典的复合二项风险模型是精算文献中研究的最深入的一类离散时间更新过程,模型的独立增量性使得数学处理极为方便,但是与保险的实际不相符合.近年来,在索赔剩余过程中引入某种相依结构受到越来越多的关注.研究了一类索赔时间相依的离散时间风险模型,模型中假设每次主索赔一定可以引起一类副索赔,同时根据索赔额的大小引起另一类副索赔,并且副索赔有可能延迟发生.通过引入3个辅助模型,研究了有限时间生存概率的母函数,并且对任意初始资本得到了有限时间内生存概率的递推表达式.

Finite time survival probability for a discrete time risk model with delayed claims

The classical compound Binomial risk model is discrete time renewal process which has been studied deeply in actuarial literature. Although the independent increment property assumed in the model is convenient to mathematical treatment, it is not consistent with insurance actual. Recently the risk processes with dependence structure have received more and more attention. In this paper a discrete time model with time-correlated claims is studied. It is assumed that every main claim can induce one kind of by-claim with certainty and another kind of by-claim according to the claim a- mount. The by-claims can be delayed to the next period. By introducing three auxiliary models, we investigate the generating function for the finite time survival probability and a recursive solution is al- so obtained for arbitrary initial surplus.