Finance and Stochastics

, Volume 8, Issue 4, pp 531–552 | Cite as

Vector-valued coherent risk measures

  • Elyés Jouini
  • Moncef Meddeb
  • Nizar Touzi


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.


Coherent risk measures liquidity risk risk aggregation 


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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.CEREMADEUniversité Paris Dauphine, and CRESTParis CédexFrance
  2. 2.CERMSEMUniversité Paris Panthéon-SorbonneParis CédexFrance
  3. 3.CREST Laboratoire de Finance et Assurance, and CEREMADEMalakof CedexFrance

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