Abstract. . This paper aims to establish the eect of the choice of a stability bound for the ruin probability on the quality of the approximation of the characteristics (ruin probabilities) of two classical risk models to approach (ideal an perturbed models) regarding to dierent large claims. In particular, we use two versions of the strong stability method: strong stability of a Markov chain and strong stability of a Lindley process. A comparative study, based on numerical results obtained by simulation, is performed between the two versions .

Resume. Ce travail porte sur l'etude de l'eet du choix de la borne de stabilite pour la probabilite de ruine sur la qualite de l'approximation des caracteristiques (probabilites de ruine) de deux modeles de risque classiques a approcher (modele ideal et modele perturbe) par rapport a dierentes reclamations larges. Particulierement, on utilise deux versions de la methode de stabilite forte: stabilite forte d'une cha^ne de Markov et stabilite forte d'un processus de Lindley. Une etude comparative, basee sur des resultats numeriques obtenus par simulation, est eectuee entre ces deux versions.

Key words: Risk model, perturbation, ruin probability, strong stability, large claim, simulation.