## Özet

We present a new numerical method to obtain the finite- and infinite-horizon ruin probabilities for a general continuous-time risk problem. We assume the claim arrivals are modeled by the versatile Markovian arrival process, the claim sizes are PH-distributed, and the premium rate is allowed to depend on the instantaneous risk reserve in a piecewise-constant manner driven by a number of thresholds, i.e., multi-threshold premiums. We introduce a novel sample path technique by which the ruin problems are shown to reduce to the steady-state solution of a certain multi-regime Markov fluid queue. We propose to use the already existing numerically efficient and stable numerical algorithms for such Markov fluid queues. Numerical results are presented to validate the effectiveness of the proposed method regarding the computation of the finite- and infinite-horizon ruin probabilities for risk models including those with relatively large number of thresholds.

Orijinal dil | İngilizce |
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Sayfa (başlangıç-bitiş) | 85-99 |

Sayfa sayısı | 15 |

Dergi | Annals of Operations Research |

Hacim | 252 |

Basın numarası | 1 |

DOI'lar | |

Yayın durumu | Yayınlandı - 1 May 2017 |

Harici olarak yayınlandı | Evet |

### Bibliyografik not

Publisher Copyright:© 2016, Springer Science+Business Media New York.

### Finansman

This work is supported in part by TUBITAK (The Scientific and Technological Research Council of Turkey) Project No. 115E360. We also thank the two editors and the three anonymous reviewers for their insightful comments on the paper which have helped improve the manuscript in terms of both content and presentation.

Finansörler | Finansör numarası |
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TUBITAK | |

Türkiye Bilimsel ve Teknolojik Araştirma Kurumu | 115E360 |