保费随机复合二项模型的Gerber-shiu折现罚金函数  

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

作　　者：孙歆[1,2] 方世祖[2] 段誉[1] 

机构地区：[1]毕节学院数学系,贵州毕节551700 [2]广西大学数学与信息科学学院,广西南宁530004

出　　处：《经济数学》2010年第4期73-80,共8页Journal of Quantitative Economics

基　　金：贵州教育厅基金项目(2007079);毕节学院自然科学基金项目(20092017)

摘　　要：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.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.

关 键 词：复合二项模型 GERBER-SHIU折现罚金函数 瑕疵更新方程 复合几何分布 

分 类 号：O211.67[理学—概率论与数理统计]