Vector-valued coherent risk measures

We define (d, n) -coherent risk measures as set-valued maps from L-d(infinity) into R-n satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from R-d-valued random portfolio to R-n-valued measure of risk. Necessary and sufficient condition's of coherent aggregation are provided.