We define (d, n)−coherent risk measures as set-valued maps from L ∞ d into IRn sat-We show that this definition is a convenient extension of the isfying some axioms. real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from IR d−valued random portfolio to IR n−valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.
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