Risk measures and multivariate extensions of Breiman's Theorem

Anne-Laure Fougères (1) , Cécile Mercadier (1)

1 PSPM - Probabilités, statistique, physique mathématique

Modeling insurance risks is a task that received an increasing attention because of Solvency Capital Requirements. The ruin probability has become a standard risk measure to assess regulatory capital. In this paper we focus on discrete time models for nite time horizon. Several results are available in the literature allowing to calibrate the ruin probability by means of the sum of the tail probabilities of individual claim amounts. The aim of this work is to obtain asymptotics for such probabilities under multivariate regularly variation and, more precisely, to derive them from Breiman's Theorem extensions. We thus exhibit new situations where the ruin probability admits computable equivalents. Consequences are also derived in terms of the Value-at-Risk.

Mots clés: Discrete time model; Ruin probability; Value-at-Risk; Multivariate regular variation; Dependent risks

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Anne-Laure Fougères, Cécile Mercadier. Risk measures and multivariate extensions of Breiman's Theorem. Journal of Applied Probability, 2012, 49 (2), pp.364-384. ⟨10.1239/jap/1339878792⟩. ⟨hal-00487860⟩