Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory

被引：42
作者：
Qihe Tang
Gurami Tsitsiashvili
机构：
[1] University of Amsterdam,Department of Quantitative Economics
[2] Russian Academy of Sciences,Institute of Applied Mathematics, Far Eastern Scientific Center
来源：
Extremes | 2003年 / 6卷 / 3期
关键词：
asymptotics; dominated variation; ruin probability; subexponentiality; uniformity;
D O I：
10.1023/B:EXTR.0000031178.19509.57
中图分类号：
学科分类号：
摘要：
Let {Xk, 1 ≤ k ≤ n} be n independent and real-valued random variables with common subexponential distribution function, and let {θk, 1 ≤ k ≤ n} be other n random variables independent of {Xk, 1 ≤ k ≤ n} and satisfying a ≤ θk ≤ b for some 0 < a ≤ b < ∞ for all 1 ≤ k ≤ n. This paper proves that the asymptotic relations P (max1 ≤ m ≤ n ∑k=1m θkXk > x) ∼ P (sumk=1n θkXk > x) ∼ sumk=1nP (θkXk > x) hold as x → ∞. In doing so, no any assumption is made on the dependence structure of the sequence {θk, 1 ≤ k ≤ n}. An application to ruin theory is proposed.
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页码：171 / 188
页数：17
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