Asymptotic tail behavior of Poisson shot-noise processes with interdependence between shock and arrival time

被引：2

作者：

Li, Xiaohu ^{[1
,2
]}

Wu, Jintang ^{[2
]}

机构：

[1] Univ New Orleans, Dept Math, New Orleans, LA 70148 USA

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2014年 / 88卷

基金：

中国国家自然科学基金;

关键词：

Asymptotic independence; Copula; Multivariate regular varying; Tail equivalence; SUBEXPONENTIALITY; DEPENDENCE; PRODUCT; SUMS;

D O I：

10.1016/j.spl.2014.01.026

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper studies the tail behavior of the Poisson shot-noise processes with interdependent and heavy-tailed random shocks. In the presence of statistical dependence between the shock and its arrival time we establish the asymptotic behavior of the tail probability. Two examples are presented as illustrations of the main results as well. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：15 / 26

页数：12

共 21 条

[1] Exponential behavior in the presence of dependence in risk theory [J].

Albrecher, H ;

Teugels, JL .

JOURNAL OF APPLIED PROBABILITY, 2006, 43 (01) :257-273

[2] A ruin model with dependence between claim sizes and claim intervals [J].

Albrecher, H ;

Boxma, OJ .

INSURANCE MATHEMATICS & ECONOMICS, 2004, 35 (02) :245-254

[3]

[Anonymous], 2006, An introduction to copulas

[4]

[Anonymous], 2006, P IEEE MIL COMM C

[5] Ruin probabilities for a regenerative Poisson gap generated risk process [J].

Asmussen S. ;

Biard R. .

European Actuarial Journal, 2011, 1 (1) :3-22

[6] On the tail behavior of sums of dependent risks [J].

Barbe, Philippe ;

Fougeres, Anne-Laure ;

Genest, Christian .

ASTIN BULLETIN, 2006, 36 (02) :361-373

[7] Regular variation of GARCH processes [J].

Basrak, B ;

Davis, RA ;

Mikosch, T .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 99 (01) :95-115

[8] Asymptotic finite-time ruin probabilities for a class of path-dependent heavy-tailed claim amounts using Poisson spacings [J].

Biard, Romain ;

Lefevre, Claude ;

Loisel, Stephane ;

Nagaraja, Haikady N. .

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, 2011, 27 (05) :503-518

[9] An insensitivity property of Lundberg's estimate for delayed claims [J].

Brémaud, P .

JOURNAL OF APPLIED PROBABILITY, 2000, 37 (03) :914-917

[10] SUBEXPONENTIALITY OF THE PRODUCT OF INDEPENDENT RANDOM-VARIABLES [J].

CLINE, DBH ;

SAMORODNITSKY, E .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1994, 49 (01) :75-98

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