Vector-Valued Risk Measure Processes

Introduced by Artzner, Delbaen, Eber and Heath (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini, Meddeb and Touzi (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results, we study different notions of time consistency and we give examples of vector-valued risk measure processes