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The density of the time of ruin in the classical risk model with a constant dividend barrier

Published online by Cambridge University Press:  04 November 2013

Shuanming Li  and
Yi Lu
Shuanming Li
Affiliation:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Australia
Yi Lu
Affiliation:
Department of Statistics and Actuarial Science, Simon Fraser University, Canada
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Abstract

In this paper, we investigate the density function of the time of ruin in the classical risk model with a constant dividend barrier. When claims are exponentially distributed, we derive explicit expressions for the density function of the time of ruin and its decompositions: the density of the time of ruin without dividend payments and the density of the time of ruin with dividend payments. These densities are obtained based on their Laplace transforms, and expressed in terms of some special functions which are computationally tractable. The Laplace transforms are being inverted using a magnificent tool, the Lagrange inverse formula, developed in Dickson and Willmot (2005). Several numerical examples are given to illustrate our results.

Keywords

Classical risk modelconstant dividend barrierfinite-time ruin probabilityLaplace transformstransform inversion relationship
Type
Papers
Information
Annals of Actuarial Science , Volume 8 , Issue 1 , March 2014 , pp. 63 - 78
Copyright
Copyright © Institute and Faculty of Actuaries 2013 

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