On the accuracy of phase-type approximations of heavy-tailed risk models

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Abstract

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages24
Publication statusPublished - 2012

Publication series

NameReport Eurandom
Volume2012010
ISSN (Print)1389-2355

Fingerprint

Ruin Probability
Approximation
Completely Monotone
Phase-type Distribution
Probability of Ruin
Heavy Traffic
Heavy Tails
Evaluation
Model
Error Bounds
Excess
Estimate

Cite this

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title = "On the accuracy of phase-type approximations of heavy-tailed risk models",
abstract = "Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.",
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Vatamidou, E, Adan, IJBF, Vlasiou, M & Zwart, AP 2012, On the accuracy of phase-type approximations of heavy-tailed risk models. Report Eurandom, vol. 2012010, Eurandom, Eindhoven.

On the accuracy of phase-type approximations of heavy-tailed risk models. / Vatamidou, E.; Adan, I.J.B.F.; Vlasiou, M.; Zwart, A.P.

Eindhoven : Eurandom, 2012. 24 p. (Report Eurandom; Vol. 2012010).

Research output: Book/ReportReportAcademic

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