ON THE DISTRIBUTIONS OF THE SUP AND INF OF THE CLASSICAL RISK PROCESS WITH EXPONENTIAL CLAIM*

Abstract. The purpose of this article is to use the double Laplace transform of the occupation measure of the classical risk process X with exponential claim to deduce the distributions of the random variables sup{Xs: s ≤ t} and inf{Xs: s ≤ t}, for every t> 0. As a consequence, we also get the distributions of the time to ruin in finite time and the first passage of a given level. 1