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Some Explicit Solutions for the Joint Density of the Time of Ruin and the Deficit at Ruin

Published online by Cambridge University Press:  17 April 2015

David C.M. Dickson
David C.M. Dickson*
Affiliation:
Centre for Actuarial Studies, Department of Economics, University of Melbourne, Victoria 3010, Australia, E-Mail: [email protected]
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Abstract

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Using probabilistic arguments we obtain an integral expression for the joint density of the time of ruin and the deficit at ruin. For the classical risk model, we obtain the bivariate Laplace transform of this joint density and invert it in the cases of individual claims distributed as Erlang(2) and as a mixture of two exponential distributions. As a consequence, we obtain explicit solutions for the density of the time of ruin.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 1 , May 2008 , pp. 259 - 276
Copyright
Copyright © ASTIN Bulletin 2008

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