Performance analysis with truncated heavy-tailed distributions
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/212942
- author
- Asmussen, S and Pihlsgård, Mats LU
- organization
- publishing date
- 2005
- 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
- Springer
- 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
- 2016-04-01 12:25:01
- date last changed
- 2022-01-27 03:27:26
@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}},
keywords = {{regular variation; ruin probability; insurance risk; M/G/1 queue; Levy; process}},
language = {{eng}},
number = {{4}},
pages = {{439--457}},
publisher = {{Springer}},
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}},
doi = {{10.1007/s11009-005-5002-1}},
volume = {{7}},
year = {{2005}},
}