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Explicit Solutions for Survival Probabilities in the Classical Risk Model

Published online by Cambridge University Press:  17 April 2015

Jorge M.A. Garcia
Jorge M.A. Garcia*
Affiliation:
CEMAPRE, ISEG, Technical University of Lisbon, Rua do Quelhas, 2 1200-781 Lisboa, Portugal, E-mail: jorgegarcia@iseg.utl.pt
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Abstract

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The purpose of this paper is to show that, for the classical risk model, explicit expressions for survival probabilities in a finite time horizon can be obtained through the inversion of the double Laplace transform of the distribution of time to ruin. To do this, we consider Gerber and Shiu (1998) and a particular value for their penalty function. Although other methods to address the problem exist, we find this approach, perhaps, more direct and simple. For the analytic inversion, we have applied twice, after some algebra, the Laplace complex inversion formula.

Keywords

Classical risk modeldouble Laplace transformTime to ruinRuin probabilities
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 1 , May 2005 , pp. 113 - 130
Copyright
Copyright © ASTIN Bulletin 2005

References

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