On Upper Bounds for the Tail Distribution of Geometric Sums of Subexponential Random Variables

2008/05/29 by Andrew Richards, Richards, Andrew
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #46N30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:46N30

paper · pdf · doi:10.48550/arxiv.0805.4548

14 pages, 4 figures

openalex publication_date 2008/05/29 · arxiv created 2009/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The approach used by Kalashnikov and Tsitsiashvili for constructing upper bounds for the tail distribution of a geometric sum with subexponential summands is reconsidered. By expressing the problem in a more probabilistic light, several improvements and one correction are made, which enables the constructed bound to be significantly tighter. Several examples are given, showing how to implement the theoretical result.

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