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. Keywords: ruin probability, heavy-tailed claim sizes, completely monotone distribution, spectral function, hyperexponential distribution, error bounds
Original languageEnglish
Pages (from-to)510-534
Number of pages25
JournalScandinavian Actuarial Journal
Volume2014
Issue number6
DOIs
Publication statusPublished - 2014

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Ruin Probability
Completely Monotone
Approximation
Error Bounds
Phase-type Distribution
Probability of Ruin
Heavy Traffic
Heavy Tails
Model
Spectral Function
Evaluation
Excess
Risk model
Ruin probability
Estimate
Error bounds

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. Keywords: ruin probability, heavy-tailed claim sizes, completely monotone distribution, spectral function, hyperexponential distribution, error bounds",
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On the accuracy of phase-type approximations of heavy-tailed risk models. / Vatamidou, E.; Adan, I.J.B.F.; Vlasiou, M.; Zwart, A.P.

In: Scandinavian Actuarial Journal, Vol. 2014, No. 6, 2014, p. 510-534.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - On the accuracy of phase-type approximations of heavy-tailed risk models

AU - Vatamidou, E.

AU - Adan, I.J.B.F.

AU - Vlasiou, M.

AU - Zwart, A.P.

PY - 2014

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AB - 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. Keywords: ruin probability, heavy-tailed claim sizes, completely monotone distribution, spectral function, hyperexponential distribution, error bounds

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DO - 10.1080/03461238.2012.729154

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