Finance and Stochastics

, Volume 8, Issue 4, pp 531–552

Vector-valued coherent risk measures

Authors

    • CEREMADEUniversité Paris Dauphine, and CREST
  • Moncef Meddeb
    • CERMSEMUniversité Paris Panthéon-Sorbonne
  • Nizar Touzi
    • CREST Laboratoire de Finance et Assurance, and CEREMADE
Article

DOI: 10.1007/s00780-004-0127-6

Cite this article as:
Jouini, E., Meddeb, M. & Touzi, N. Finance and Stochastics (2004) 8: 531. doi:10.1007/s00780-004-0127-6

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.

Keywords:

Coherent risk measuresliquidity riskrisk aggregation

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004