Advances in Applied Probability

Weighted sums of subexponential random variables and their maxima

Yiqing Chen, Kai W. Ng, and Qihe Tang

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Let {Xk, k=1,2,...} be a sequence of independent random variables with common subexponential distribution F, and let {wk, k=1,2,...} be a sequence of positive numbers. Under some mild summability conditions, we establish simple asymptotic estimates for the extreme tail probabilities of both the weighted sum ∑k=1nwkXk and the maximum of weighted sums max1≤mnk=1mwkXk, subject to the requirement that they should hold uniformly for n=1,2,.... Potentially, a direct application of the result is to risk analysis, where the ruin probability is to be evaluated for a company having gross loss Xk during the kth year, with a discount or inflation factor wk.

Article information

Adv. in Appl. Probab. Volume 37, Number 2 (2005), 510-522.

First available in Project Euclid: 15 June 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E20
Secondary: 60G50: Sums of independent random variables; random walks 60G70: Extreme value theory; extremal processes

Asymptotics Matuszewska index weighted sum maximum subexponentiality tail probability uniformity ruin probability discounted loss


Chen, Yiqing; Ng, Kai W.; Tang, Qihe. Weighted sums of subexponential random variables and their maxima. Adv. in Appl. Probab. 37 (2005), no. 2, 510--522. doi:10.1239/aap/1118858636.

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