
Law Invariant Risk Measures Have the Fatou Property
Touzi, Nizar; Schachermayer, Walter; Jouini, Elyès (2006), Law Invariant Risk Measures Have the Fatou Property, in Yamazaki, Akira; Kusuoka, Shigeo, Advances in Mathematical Economics, volume 9, Springer : Tokyo, p. 49-71
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Type
Chapitre d'ouvrageExternal document link
http://halshs.archives-ouvertes.fr/halshs-00176522/en/Date
2006Book title
Advances in Mathematical Economics, volume 9Book author
Yamazaki, Akira; Kusuoka, ShigeoPublisher
Springer
Published in
Tokyo
ISBN
978-4-431-34341-7
Number of pages
136Pages
49-71
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Show full item recordAbstract (EN)
S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02]. In thepresent note we extend Kusuoka's characterization in two directions, thefirst one being rather standard, while the second one is somewhat surprising. Firstly we generalize — similarly as M. Fritelli and E. Rossaza Gianin [FG05] — from the notion of coherent risk measures to the more general notion of convex risk measures as introduced by H. F¨ollmer and A. Schied [FS 04]. Secondly — and more importantly — we show that the hypothesis of Fatou property may actually be dropped as it is automatically implied by the hypothesis of law invariance.We also introduce the notion of the Lebesgue property of a convex risk measure, where the inequality in the definition of the Fatou property is replaced by an equality, and give some dual characterizations of this property.Subjects / Keywords
risk measures; Fatou propertyRelated items
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