Precise large deviation result for heavy-tailed random sums and applications to risk theory  

重尾随机和的精致大偏差及其在风险理论中的应用(英文)

作　　者：杨洋[1,2] 林金官[1] 

机构地区：[1]东南大学数学系,南京211189 [2]南京审计学院数学与统计学院,南京210029

出　　处：《Journal of Southeast University(English Edition)》2010年第3期498-501,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China (No.10671139,11001052);the Natural Science Foundation of Jiangsu Province(No. BK2008284 );China Postdoctoral Science Foundation ( No.20100471365);the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (No. 09KJD110003);Postdoctoral Research Program of Jiangsu Province (No.0901029C)

摘　　要：The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.对2列非负带有次指数分布的独立同分布随机变量的差,以及随机脚标为负相协随机变量生成的严平稳更新记数过程进行了探讨.利用修正的随机变量部分和的精致大偏差结果及关于负相协随机变量的基本更新定理和中心极限定理,得到了随机变量列差的随机和的精致大偏差.考虑了基于顾客来到过程的保险风险模型,利用随机和的精致大偏差结果,得到了当顾客数或者时间趋于无穷时,保险公司破产概率的一致渐近性.

关 键 词：precise large deviation random sum sub-exponential distribution renewal counting process customer-arrival-based insurance risk model 

分 类 号：O211.4[理学—概率论与数理统计]