˖ڍመڙጲ
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二维重尾相依风险模型的精细大偏差
田海兰 ，沈新美
大连理工大学 数学科学学院，大连 116024
摘要：令{
~
X
k
, k ≥ 1}为一列独立同分布二维非负随机向量, 边际分布为F
1
, F
2
, 均服从ERV 族,
联合分布为F
1,2
, 有限均值向量~µ = E
~
X
1
. 本文允许
~
X
1
的分量相依. 在一些温和的条件下, 本文
讨论了部分和
~
S
n
=
P
n
k=1
~
X
k
和随机和
~
S
N(t)
=
P
N(t)
k=1
~
X
k
的精细大偏差, 其中N(t)是一个
与{
~
X
k
, k ≥ 1}相互独立的计数过程
关键词：精细大偏差, ERV族,连接函数,随机和
中图分类号： 60G50; 62P05; 60F10.
Precise large deviations for sums of
two-dimensional random vectors with dependent
components with extended regularly varying tails
TIAN Hai-Lan , SHEN Xin-Mei
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024
Abstract: Let {
~
X
k
, k ≥ 1} be a sequence of independent identically distributed non-negative
random vectors with common marginal distributions F
1
, F
2
having extended regularly varying
tails, joint distribution function F
1,2
and finite mean ~µ = E
~
X
1
. The two components of
~
X
1
are allowed to be dependent. Under some mild assumptions, precise large deviations for both
the partial sums
~
S
n
=
P
n
k=1
~
X
k
and the random sums
~
S
N(t)
=
P
N(t)
k=1
~
X
k
are investigated,
where N(t) is a counting process independent of the sequence {
~
X
k
, k ≥ 1}.
Key words: precise large deviations, extended regular variation distributions, copula
functions, random sums.
0 Introduction
Large deviation probabilities occur in a natural way in many applied areas, for instance,
insurance and finance. Up to now, many researchers have made great efforts of the precise
基金项目： Fund for the Doctor Program of Higher Education(No. 20100041120038)
作者简介： TIAN Hai-Lan（1986-），female，postgraduate，major research direction：Heavy tailed distributions
in the presence of dependence. Correspondence author：SHEN Xin-Mei（1981-），female，lecturer，major research
direction：Risk theory.
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