Performance Analysis with Truncated Heavy-Tailed Distributions

Søren Asmussen () and Mats Pihlsgård ()
Additional contact information
Søren Asmussen: Aarhus University
Mats Pihlsgård: Lund University

Methodology and Computing in Applied Probability, 2005, vol. 7, issue 4, 439-457

Abstract: Abstract This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U ∧ K 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 (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-005-5002-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:7:y:2005:i:4:d:10.1007_s11009-005-5002-1

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-005-5002-1

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().