Explicit Solutions for Survival Probabilities in the Classical Risk Model

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 reconsider 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.