保费随机复合二项模型的Gerber-shiu折现罚金函数

考虑保费随机收取的复合二项模型.得到了其Gerber-shiu折现罚金函数满足的递推公式,瑕疵更新方程及其渐近解,并且通过构造一个相关的复合几何分布函数,得到了这个更新方程的解析解.相应的也得到了一些相关精算量的渐近表示和分布函数,如破产前瞬时盈余分布的渐近解,导致破产的索赔额的分布函数.

The Gerber-Shiu Discounted Penalty Function in the Compound Binomial Risk Model with Random Income

Considering a compound binomial model with random income,a recursive formula was derived for the Gerber-Shiu discounted penalty function,and the asymptotic estimate of the Gerber-Shiu discounted penalty function was discussed.Furthermore,an explicit formula for the Gerber-Shiu penalty function was given in terms of a compound geometric distribution function,through which many related quantities were analyzed,e.g.,the asymptotic estimate of the surplus before ruin,and the distribution of the claim causing ruin.