Finite time ruin probabilities with one Laplace inversion

Florin Avram, Miguel Usabel

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)371-377
Number of pages7
JournalInsurance: Mathematics and Economics
Volume32
Issue number3
DOIs
Publication statusPublished - 21 Jul 2003

Keywords

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

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