风险模型中重尾随机变量和的若干大偏差结果

Some Large Deviation Results for Sums of Heavy-tailed Random Variables in the Risk Models

进一步研究随机变量部分和与随机和的大偏差,其中S(n)=∑ni=1Xi,S(t)=∑N(t)i=1Xi(t>0).{Xn,n≥1}是一个独立同分布的随机变量(未必是非负的)序列具有共同的分布F(定义于R上)和有限期望μ=EX1.{N(t),t≥0}是一个非负的整数值的随机变量的更新计数过程且与{Xn,n≥1}相互独立.本文在假定F∈C条件下,进一步推广并改进了由Klüppelberg等和Kaiw等人给出的一些大偏差结果.这些结果可应用到某些金融保险方面的一些特定的问题中去.

This paper investigates large deviation for partial and random sums of random variables where { Xn, n≥ 1 } are independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ = EX1. {N （t）, t≥0} is a renewal counting process of non-negative integer valued random variables, N（t） independent of （Xn,n≥1}, S（n）=i=1∑nXi,S（t）=i=1∑n（xi（t〉0） Suppose F∈C, this paper furhter extended and improved the some large deviation results by Kluppelberg et. al. and Kaiw et. al. These results can applies to certain problems in insurance and finance.