Explicit Solutions for Survival Probabilities in the Classical Risk Model

Jorge M.A. Garcia
2005 ASTIN Bulletin: The Journal of the International Actuarial Association  
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
more » ... ersion, we have applied twice, after some algebra, the Laplace complex inversion formula.
doi:10.2143/ast.35.1.583168 fatcat:ehx2wdl7fvgdpji2gbdolkr5ju