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 and ruin 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 follow Gerber and Shiu (1998). Although other methods for such question do exist, we found this approach more direct and simple. The method for determination of the transform follows Dickson (2001). For the analitic inversion, we have applied twice, after some algebra, the Laplace complex inversion formula.

Keywords: Classical risk model; double Laplace transform; Time to ruin; Survival probability