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Arbitrage and state price deflators in a general intertemporal framework

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Date
2005
Link to item file
http://halshs.archives-ouvertes.fr/halshs-00151526/en/
Dewey
Economie financière
Sujet
Investment Opportunities; Asset Pricing; Free Lunch; State Price Deflators; Arbitrage
JEL code
E31; G12; G11
Journal issue
Journal of Mathematical Economics
Volume
41
Number
6
Publication date
09-2005
Article pages
722-734
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jmateco.2004.06.001
URI
https://basepub.dauphine.fr/handle/123456789/345
Collections
  • DRM : Publications
  • CEREMADE : Publications
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Author
Napp, Clotilde
Jouini, Elyès
Type
Article accepté pour publication ou publié
Abstract (EN)
In securities markets, the characterization of the absence of arbitrage by the existence of state price deflators is generally obtained through the use of the Kreps–Yan theorem.This paper deals with the validity of this theorem (see Kreps, D.M., 1981. Arbitrage and equilibrium in economies with infinitely many commodities. Journal of Mathematical Economics 8, 15–35; Yan, J.A., 1980. Caractérisation d'une classe d'ensembles convexes de L1 ou H1. Sém. de Probabilités XIV. Lecture Notes in Mathematics 784, 220–222) in a general framework. More precisely, we say that the Kreps–Yan theorem is valid for a locally convex topological space (X,?), endowed with an order structure, if for each closed convex cone C in X such that CX? and C?X+={0}, there exists a strictly positive continuous linear functional on X, whose restriction to C is non-positive.We first show that the Kreps–Yan theorem is not valid for spaces if fails to be sigma-finite.Then we prove that the Kreps–Yan theorem is valid for topological vector spaces in separating duality X,Y, provided Y satisfies both a “completeness condition” and a “Lindelöf-like condition”.We apply this result to the characterization of the no-arbitrage assumption in a general intertemporal framework.

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