# Vector-valued coherent risk measures

## Author

Listed:
• 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

## Suggested Citation

• Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
• Handle: RePEc:spr:finsto:v:8:y:2004:i:4:p:531-552
DOI: 10.1007/s00780-004-0127-6
as

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

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## References listed on IDEAS

as
1. Damir Filipovic & Michael Kupper, 2007. "On the Group Level Swiss Solvency Test," Research Paper Series 188, Quantitative Finance Research Centre, University of Technology, Sydney.
2. Dana, Rose-Anne & Scarsini, Marco, 2007. "Optimal risk sharing with background risk," Journal of Economic Theory, Elsevier, vol. 133(1), pages 152-176, March.
3. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292.
4. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
5. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
6. repec:dau:papers:123456789/361 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

### Keywords

Coherent risk measures; liquidity risk; risk aggregation;

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