Some remarks on the ruin problem in case the epochs of claims form a renewal process

Abstract

In a paper [1] ¹ Numbers in square brackets refer to the list of references at the end of the present paper. View all notes to the XVth International Congress of Actuaries, New York, 1957, E. Sparre Andersen presented a model of a collective risk process with a positive gross risk premium where the epochs of claims formed a renewal process. Assuming this model the present author shows that it is possible to obtain generalizations of the explicit formulas given by Cramér [6] for the Poisson case.