Vector-valued coherent risk measures

@article{Jouini2004VectorvaluedCR,
  title={Vector-valued coherent risk measures},
  author={E. Jouini and M. Meddeb and N. Touzi},
  journal={Finance and Stochastics},
  year={2004},
  volume={8},
  pages={531-552}
}
  • E. Jouini, M. Meddeb, N. Touzi
  • Published 2004
  • Mathematics, Computer Science
  • Finance and Stochastics
  • 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. 
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