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Vector-valued coherent risk measures

We define (d,n)-coherent risk measures as set-valued maps from L (exponential infinity) (subscript n) into R (exponential n) satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. We then discuss the aggregation is...

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Bibliographic Details
Published in:Finance and stochastics 2004-11, Vol.8 (4), p.531-552
Main Authors: Jouini, Ely s, Meddeb, Moncef, Touzi, Nizar
Format: Article
Language:English
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Summary:We define (d,n)-coherent risk measures as set-valued maps from L (exponential infinity) (subscript n) into R (exponential n) satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. We then discuss the aggregation issue, i.e., the passage R (exponential d) from valued random portfolio to R (exponential n) valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided. [PUBLICATION ABSTRACT]
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-004-0127-6