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

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

11 Citaten (Scopus)
3 Downloads (Pure)

Samenvatting

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
Originele taal-2Engels
Pagina's (van-tot)510-534
Aantal pagina's25
TijdschriftScandinavian Actuarial Journal
Volume2014
Nummer van het tijdschrift6
DOI's
StatusGepubliceerd - 2014

Vingerafdruk Duik in de onderzoeksthema's van 'On the accuracy of phase-type approximations of heavy-tailed risk models'. Samen vormen ze een unieke vingerafdruk.

  • Citeer dit