Explicit finite-time and infinite-time ruin probabilities in the continuous case

Abstract

In this rather self-contained paper we indicate general explicit analytic expressions for finite-time and infinite-time ruin probabilities in the classical risk model corresponding to initial risk reserves u≥0. We assume that the claimsize distribution has a density on [0,∞). Our solutions are continuous versions of discrete expressions by Picard and Lefèvre but our methodology is different and the continuous formulas have a component with no counterpart in the discrete case [cf. Picard, P., Lefèvre, C., 1997. The probability of ruin in finite time with discrete claim size distribution. Scandinavian Actuarial Journal 1, 58–69].