古典风险模型下盈余过程的相关分析  

Relation analysis of a surplus process in the classical model

作　　者：刘次华[1] 陈卓恒[1] 

机构地区：[1]华中科技大学数学系,湖北武汉430074

出　　处：《华中科技大学学报（自然科学版）》2005年第10期109-111,共3页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10301011)

摘　　要：讨论了古典风险模型的盈余过程和盈余通过给定水平时间的一些性质,运用鞅论和随机游动的方法得到了破产前盈余通过给定水平的概率Pa的近似表达式及其精细估计.当索赔额服从指数分布时,给出了具体实例.随后在不考虑破产的情况下,使用更简单的办法得出了盈余首次通过水平a时刻的期望的精确表达式,并从实际出发进一步在考虑破产时得到这个条件期望的上界.This paper discussed the surplus process in the classical model and considered the hitting times Using martingales and random walks, the author got an approximate formula about probability of that the insurer＇s surplus reaches an upper barrier before the ruin and its precise estimation. If the distribution of the claim count is exponential, the author got the example. And the author used a simpler method to obtain the exact formula of expectation of hitting times, unconditionally on the event that ruin did not occur before the surplus had exceeded. At the same time. upper barrier of the conditional expectation of first passage times was given if ruin in practice was considered.

关 键 词：盈余过程 随机游动 条件概率 停时 鞅 

分 类 号：O211.6[理学—概率论与数理统计]