Probabilite de ruine eventuelle dans un modele de risque a temps discret.

We continue the study of the discrete-time risk model introduced by Picard et al. (2003). The cumulative loss process (St)t (element of) N has independent and stationary increments, the increments per unit of time having nonnegative integer values with distribution {ai, i (element of) N} and mean a. The premium receipt process (ck)k (element of) N is deterministic, nonnegative and nonuniform; in addition, we assume it to be regular in order for there to exist a constant c > a such that the deviation (sigma) (ckc) is bounded as the time t varies. We are interested in whether or not ruin occurs within a finite time. If T is the time of ruin, we obtain P(T=(infinity)) as the limit of P(T>t) as t - (infinity), firstly in the particular case where c = 1/d for some positive d (element of) N, and then in the general case for positive c under the condition that a0 > ½.