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On the Density and Moments of the Time of Ruin with Exponential Claims

Published online by Cambridge University Press:  17 April 2015

Steve Drekic  and
Gordon E. Willmot
Steve Drekic
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, E-mail: sdrekic@math.uwaterloo.ca, gewillmo@icarus.uwaterloo.ca
Gordon E. Willmot
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, E-mail: sdrekic@math.uwaterloo.ca, gewillmo@icarus.uwaterloo.ca
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Abstract

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The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.

Keywords

Laplace transformBessel functionGauss hypergeometric seriesGerber-Shiu equationcompound geometric tailruin probability
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 1 , May 2003 , pp. 11 - 21
Copyright
Copyright © ASTIN Bulletin 2003

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