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Performance analysis with truncated heavy-tailed distributions

Asmussen, S and Pihlsgård, Mats LU (2005) In Methodology and Computing in Applied Probability 7(4). p.439-457
Abstract
This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U boolean AND 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 EU. We study the compound Poisson ruin probability psi(u) or, equivalently, the tail P(W > u) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of psi(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 psi(u) in order to figure out the threshold between the light-tailed... (More)
This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U boolean AND 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 EU. We study the compound Poisson ruin probability psi(u) or, equivalently, the tail P(W > u) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of psi(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 psi(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 -> infinity of the asymptotic exponential decay rate gamma = gamma((K)) in a more general truncated Levy process setting, and give a discussion of some of the implications for the approximations. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
regular variation, ruin probability, insurance risk, M/G/1 queue, Levy, process
in
Methodology and Computing in Applied Probability
volume
7
issue
4
pages
439 - 457
publisher
Kluwer
external identifiers
  • wos:000233393000002
  • scopus:28944436502
ISSN
1573-7713
DOI
10.1007/s11009-005-5002-1
language
English
LU publication?
yes
id
f8768e5f-745b-4b48-a97a-436c0519a5d4 (old id 212942)
date added to LUP
2007-08-21 12:35:50
date last changed
2017-10-01 03:54:23
@article{f8768e5f-745b-4b48-a97a-436c0519a5d4,
  abstract     = {This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U boolean AND 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 EU. We study the compound Poisson ruin probability psi(u) or, equivalently, the tail P(W > u) of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of psi(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 psi(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 -> infinity of the asymptotic exponential decay rate gamma = gamma((K)) in a more general truncated Levy process setting, and give a discussion of some of the implications for the approximations.},
  author       = {Asmussen, S and Pihlsgård, Mats},
  issn         = {1573-7713},
  keyword      = {regular variation,ruin probability,insurance risk,M/G/1 queue,Levy,process},
  language     = {eng},
  number       = {4},
  pages        = {439--457},
  publisher    = {Kluwer},
  series       = {Methodology and Computing in Applied Probability},
  title        = {Performance analysis with truncated heavy-tailed distributions},
  url          = {http://dx.doi.org/10.1007/s11009-005-5002-1},
  volume       = {7},
  year         = {2005},
}