[1] Yang Yang, Lin Jinguan,. Precise large deviation result for heavy-tailed random sumsand applications to risk theory [J]. Journal of Southeast University (English Edition), 2010, 26 (3): 498-501. [doi:10.3969/j.issn.1003-7985.2010.03.026]

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Precise large deviation result for heavy-tailed random sumsand 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

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

26

Issue:

2010 3

Page:

498-501

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2010-09-30

Info

Title:

Precise large deviation result for heavy-tailed random sumsand 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

Author(s):

Yang Yang¹;  2;  Lin Jinguan¹

¹ Department of Mathematics, Southeast University, Nanjing 211189, China
² School of Mathematics and Statistics, Nanjing Audit University, Nanjing 210029, China

杨洋¹;  2;  林金官¹

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

Keywords:

precise large deviation;  random sum;  sub-exponential distribution;  renewal counting process;  customer-arrival-based insurance risk model

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

PACS:

O211.4

DOI:

10.3969/j.issn.1003-7985.2010.03.026

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.

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.

References:

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Memo

Memo:

Biographies: Yang Yang(1979—), male, doctor; Lin Jinguan(corresponding author), male, doctor, professor, jglin@seu.edu.cn.
Foundation items: 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).
Citation: Yang Yang, Lin Jinguan.Precise large deviation result for heavy-tailed random sums and applications to risk theory[J].Journal of Southeast University(English Edition), 2010, 26(3):498-501.

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