保费随机复合二项模型的Gerber-shiu折现罚金函数
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引用本文:孙 歆,方世祖,段 誉.保费随机复合二项模型的Gerber-shiu折现罚金函数[J].经济数学,2010,27(4):73-80
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作者单位
孙 歆,方世祖,段 誉 (1. 毕节学院 数学系贵州 毕节5517002. 广西大学 数学与信息科学学院广西 南宁530004) 
中文摘要: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.
中文关键词: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
 
The Gerber-Shiu Discounted Penalty Function in the Compound Binomial Risk Model with Random Income
Abstract: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.
keywords:compound binomial model  Gerber-Shiu discounted penalty function  defective renewal equation  compound geometric distribution
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