### Abstract

Original language | English |
---|---|

Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 24 |

Publication status | Published - 2012 |

### Publication series

Name | Report Eurandom |
---|---|

Volume | 2012010 |

ISSN (Print) | 1389-2355 |

### Fingerprint

### Cite this

*On the accuracy of phase-type approximations of heavy-tailed risk models*. (Report Eurandom; Vol. 2012010). Eindhoven: Eurandom.

}

*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.

Research output: Book/Report › Report › Academic

TY - BOOK

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 - 2012

Y1 - 2012

N2 - 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.

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.

M3 - Report

T3 - Report Eurandom

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

PB - Eurandom

CY - Eindhoven

ER -