Vector-valued Coherent Risk Measures

Elyès Jouini (1) , Moncef Meddeb (2) , Nizar Touzi (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique
3 CMAP - Centre de Mathématiques Appliquées

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random portofolio to valued measure of Risk. Necessary and sufficient conditions of coherent aggregation are provided

Mots clés: risk; measures

Domaines: Economies et finances

Elyès Jouini, Moncef Meddeb, Nizar Touzi. Vector-valued Coherent Risk Measures. Finance and Stochastics, 2004, 8, pp.531-552. ⟨halshs-00167154⟩