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Vector-valued coherent risk measures

Authors:	Email author" target="_blank">Elyés?Jouini Email author Moncef?Meddeb Nizar?Touzi

Institution:	(1) CEREMADE, Université Paris Dauphine, and CREST, Place du Maréchal de Lattre de Tassigny, 75116 Paris Cédex, France;(2) CERMSEM, Université Paris Panthéon-Sorbonne, Boulevard de LHôpital 106-112, 75647 Paris Cédex, France;(3) CREST Laboratoire de Finance et Assurance, and CEREMADE, Boulevard Gabriel Péri 15, 92245 Malakof Cedex, France

Abstract:	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.Received: February 2004, Mathematics Subject Classification (2000): 91B30, 46E30JEL Classification: D81, G31

Keywords:	Coherent risk measures liquidity risk risk aggregation
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