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Law Invariant Risk Measures Have the Fatou Property

dc.contributor.authorTouzi, Nizar
dc.contributor.authorSchachermayer, Walter
dc.contributor.authorJouini, Elyès
HAL ID: 6654
dc.date.accessioned2009-06-18T10:33:57Z
dc.date.available2009-06-18T10:33:57Z
dc.date.issued2006
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/342
dc.descriptionLe fichier attaché est une version également éditée dans les Cahiers de la Chaire "Les Particuliers face aux Risques" de l'Institut de Finance de Dauphine, cahier n° 5, janvier 2007
dc.language.isoenen
dc.subjectrisk measuresen
dc.subjectFatou propertyen
dc.subject.ddc332en
dc.subject.classificationjelD81en
dc.subject.classificationjelG32en
dc.titleLaw Invariant Risk Measures Have the Fatou Propertyen
dc.typeChapitre d'ouvrage
dc.description.abstractenS. 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.en
dc.identifier.citationpages49-71en
dc.relation.ispartoftitleAdvances in Mathematical Economics, volume 9en
dc.relation.ispartofeditorYamazaki, Akira
dc.relation.ispartofeditorKusuoka, Shigeo
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityTokyoen
dc.relation.ispartofdate2006
dc.relation.ispartofpages136en
dc.identifier.urlsitehttp://halshs.archives-ouvertes.fr/halshs-00176522/en/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelEconomie financièreen
dc.relation.ispartofisbn978-4-431-34341-7en


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