# Vector-valued coherent risk measures

## Author Info

• Elyés Jouini

()

• Moncef Meddeb

()

• Nizar Touzi

()

## 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. Copyright Springer-Verlag Berlin/Heidelberg 2004

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File URL: http://hdl.handle.net/10.1007/s00780-004-0127-6

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## Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 8 (2004)
Issue (Month): 4 (November)
Pages: 531-552

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 Handle: RePEc:spr:finsto:v:8:y:2004:i:4:p:531-552 Contact details of provider: Web page: http://www.springerlink.com/content/101164/ Order Information: Web: http://link.springer.de/orders.htm

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