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The Density of the Time to Ruin in the Classical Poisson Risk Model

Published online by Cambridge University Press:  17 April 2015

David C.M. Dickson  and
Gordon E. Willmot
David C.M. Dickson
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Victoria 3010, Australia
Gordon E. Willmot
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G 1
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Abstract

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We derive an expression for the density of the time to ruin in the classical risk model by inverting its Laplace transform. We then apply the result when the individual claim amount distribution is a mixed Erlang distribution, and show how finite time ruin probabilities can be calculated in this case.

Keywords

Time to ruinLaplace transformLagrange’s implicit function theoremCompound geometric distributionMixed Erlang distributionFinite time ruinTransient M/G/1 waiting time

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 1 , May 2005 , pp. 45 - 60
Copyright
Copyright © ASTIN Bulletin 2005

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