东南大学学报（英文版）2010，Vol.26Issue(3)：498-501,4.
重尾随机和的精致大偏差及其在风险理论中的应用
Precise large deviation result for heavy-tailed random sums and applications to risk theory
摘要
Abstract
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.关键词
精致大偏差/随机和/次指数分布/更新记数过程/基于顾客来到过程的保险风险模型Key words
precise large deviation/random sum/sub-exponential distribution/renewal counting process/customer-arrival-based insurance risk model分类
数理科学引用本文复制引用
杨洋,林金官..重尾随机和的精致大偏差及其在风险理论中的应用[J].东南大学学报（英文版）,2010,26(3):498-501,4.基金项目
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). （No.10671139,11001052）
