, Volume 8, Issue 4, pp 531-552

Vector-valued coherent risk measures

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We define (d,n)-coherent risk measures as set-valued maps from \(L^\infty_d\) into \(\mathbb{R}^n\) 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 \(\mathbb{R}^d-\)valued random portfolio to \(\mathbb{R}^n-\)valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.