Finite time ruin probabilities with one Laplace inversion

Florin Avram; Miguel Usabel

doi:10.1016/S0167-6687(03)00117-3

Finite time ruin probabilities with one Laplace inversion

Florin Avram, Miguel Usabel

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]-see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, 1981]-and it considers the deficit at ruin as well. © 2003 Elsevier Science B.V. All rights reserved.

Original language	English
Pages (from-to)	371-377
Number of pages	7
Journal	Insurance: Mathematics and Economics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1016/S0167-6687(03)00117-3
Publication status	Published - 21 Jul 2003

Keywords

Deficit at ruin
Finite-time ruin probability
Laplace transform
Lundberg's equation
Phase-type distribution

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10.1016/S0167-6687(03)00117-3

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title = "Finite time ruin probabilities with one Laplace inversion",

abstract = "In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]-see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, 1981]-and it considers the deficit at ruin as well. {\textcopyright} 2003 Elsevier Science B.V. All rights reserved.",

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AU - Avram, Florin

AU - Usabel, Miguel

PY - 2003/7/21

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N2 - In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]-see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, 1981]-and it considers the deficit at ruin as well. © 2003 Elsevier Science B.V. All rights reserved.

AB - In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]-see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, 1981]-and it considers the deficit at ruin as well. © 2003 Elsevier Science B.V. All rights reserved.

KW - Deficit at ruin

KW - Finite-time ruin probability

KW - Laplace transform

KW - Lundberg's equation

KW - Phase-type distribution

U2 - 10.1016/S0167-6687(03)00117-3

DO - 10.1016/S0167-6687(03)00117-3

M3 - Article

VL - 32

SP - 371

EP - 377

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 3

ER -

Finite time ruin probabilities with one Laplace inversion

Abstract

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