On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing

Christophe Dutang (1, 2) , Claude Lefèvre (3) , Stéphane Loisel (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 IRMA - Institut de Recherche Mathématique Avancée
3 ULB - Département de Mathématique [Bruxelles]

The purpose of this paper is to point out that an asymptotic rule "A+B/u" for the ultimate ruin probability applies to a wide class of dependent risk models, in discrete and continuous time. Dependence is incorporated through a mixing approach among claim amounts or claim inter-arrival times, leading to a systemic risk behavior. Ruin corresponds here either to classical ruin, or to stopping the activity after realizing that it is not pro table at all, when one has little possibility to increase premium income rate. Several special cases for which closed formulas are derived, are also investigated in some detail.

Domaines: Economies et finances; Probabilités [math.PR]

Christophe Dutang, Claude Lefèvre, Stéphane Loisel. On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing. Insurance: Mathematics and Economics, 2013, 53 (3), pp.774-785. ⟨hal-00746251v2⟩