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

In this rather self-contained paper we indicate general explicit analytic e xpressions for finite-time and infinite-time ruin probabilities in the clas sical risk model corresponding to initial risk reserves u greater than or e qual to 0. We assume that the claimsize distribution has a density on [0, i nfinity). Our solutions are continuous versions of discrete expressions by Picard and Lefevre but our methodology is different and the continuous form ulas have a component with no counterpart in the discrete case [cf. Picard, P., Lefevre, C., 1997, The probability of ruin in finite time with discret e claim size distribution. Scandinavian Actuarial Journal 1, 58-69]. (C) 19 99 Elsevier Science B.V. All rights reserved.