扰动因素下含相依索赔的复合二项风险模型

The Compound Binomial Model with Perturbation and Correlated Claims

本文研究一类带有扰动且含相依索赔的复合二项风险模型,考虑两种类型的索赔:主索赔和副索赔,主索赔以一定的概率引起副索赔且副索赔可能以一定的概率延迟到下一个时间段发生.通过引入辅助模型,利用递归等方法,得到了该模型下的Gerber-Shiu折现罚金函数和破产概率的明确表达式.最后给出了索赔额服从几何分布的数值模拟.

This paper researches the compound binomial model with perturbation and correlated claims. Two types of individual claims, the main claims and by-- claims, are considered, where by--claims are caused by main claims with a certain probability and may remain some time with a certain probability. By introducing a supplementary risk model and using recursive methods, the Gerber--Shiu discounted penalty function and the explicit expression of the ruin probability are obtained. A numerical example is given for geometrical claims.