相依风险模型中破产概率的一致渐近性  

Uniform asymptotics for ruin probability in dependent risk model

作　　者：杨洋[1,2] 黄龙[1] 

机构地区：[1]南京审计学院数学与统计学院,江苏南京210029 [2]东南大学数学系,江苏南京210096

出　　处：《江苏大学学报（自然科学版）》2011年第4期492-496,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11001052);中国博士后科学基金资助项目(20100471365);江苏省自然科学基金资助项目(BK2010480);江苏省博士后科研资助计划(0901029C)

摘　　要：为了研究相依更新风险模型中的破产问题,首先研究了负相协更新计数过程,得到了该计数过程的一个渐近性结果;进而在此基础上考虑了相依重尾更新风险模型,其中索赔时间间隔为负相协同分布的随机变量,并且索赔额为独立同分布的随机变量,其共同的分布属于强次指数分布族;利用负相协随机变量的基本更新定理,得到了保险公司的有限时破产概率在时间t∈[f(x),∞)上的一致渐近估计,以及无限时破产概率的渐近估计,推广了相应结果,其中f(x)为任意递增至无穷的非负函数.In order to investigate some ruin topics in some dependent renewal risk models,an asymptotic result on negative association renewal counting process was obtained.Based on the result,a dependent renewal risk model was considered.The claim inter-arrival times and the claim sizes were identical distribution random variables of negative and independent association,respectively,while the common distribution belonged to the strong subexponential distribution class.According to the elementary renewal theorem of negative association random variable,the uniform asymptotic estimate for the infinite-time ruin probability and the finite-time ruin probability of insurance company was obtained.The time horizon flexibly varies within t∈[f（x）,∞）,and f（x） is an arbitrary increasing nonnegative function tending to infinity.Some corresponding results were generalized.

关 键 词：破产概率 一致渐近性 重尾分布 强次指数族 负相协 

分 类 号：O211.4[理学—概率论与数理统计]