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Law invariant risk measures on L∞ (ℝd)

Ekeland, Ivar; Schachermayer, Walter (2011), Law invariant risk measures on L∞ (ℝd), Statistics & Risk Modeling, 28, 3, p. 195-225. http://dx.doi.org/10.1524/stnd.2011.1099

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Statistics & Risk Modeling
Volume
28
Number
3
Publisher
Oldenbourg Wissenschaftsverlag
Pages
195-225
Publication identifier
http://dx.doi.org/10.1524/stnd.2011.1099
Metadata
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Author(s)
Ekeland, Ivar
Schachermayer, Walter
Abstract (EN)
Kusuoka (2001) has obtained explicit representation theorems for comonotone risk measures and, more generally, for law invariant risk measures. These theorems pertain, like most of the previous literature, to the case of scalar-valued risks. Jouini, Meddeb, and Touzi (2004) and Burgert and Rüschendorf (2006) extended the notion of risk measures to the vector-valued case. Recently Ekeland, Galichon, and Henry (2009) and Rüschendorf (2006, 2010) obtained extensions of the above theorems of Kusuoka to this setting. Their results were confined to the regular case. In general, Kusuoka´s representation theorem for comonotone risk measures also involves a singular part. In the present work we give a full generalization of Kusuoka´s theorems to the vector-valued case. The singular component turns out to have a richer structure than in the scalar case.
Subjects / Keywords
Monge–Kantorovich problem; Monge–Kantorovich duality; risk measures; law invariance
JEL
D81 - Criteria for Decision-Making under Risk and Uncertainty

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