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Methodology and Computing in Applied Probability

, Volume 7, Issue 4, pp 439–457 | Cite as

Performance Analysis with Truncated Heavy-Tailed Distributions

  • Søren AsmussenEmail author
  • Mats Pihlsgård
Article

Abstract

This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form UK for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than \(\mathbb{E}U\). We study the compound Poisson ruin probability ψ(u) or, equivalently, the tail \(\mathbb{P}{\left( {W > u} \right)}\) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of ψ(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times, and compare the results to different approximations of ψ(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we investigate the asymptotics as K → ∞ of the asymptotic exponential decay rate γ = γ (K) in a more general truncated Lévy process setting, and give a discussion of some of the implications for the approximations.

Keywords

insurance risk M/G/1 queue ruin probability regular variation Lévy process 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Theoretical Statistics, Department of Mathematical SciencesAarhus UniversityAarhus CDenmark
  2. 2.Centre for Mathematical SciencesLund UniversityLundSweden

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