Elyès Jouini () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) Clotilde Napp (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) Walter Schachermayer (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)
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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, 1981, and Yan, 1980) in a general framework. More precisely, we say that the Kreps-Yan theorem is valid for a locally convex topological space (X,τ), endowed with an order structure, if for each closed convex cone C in X such that C⊇X₋ 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 L^{p}(Ω,F,P) if (Ω,F,P) 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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Paper provided by HAL in its series Post-Print with number
halshs-00176476_v1.
Length: Date of creation: 01 Sep 2005 Date of revision: Publication status: Published, Journal of Mathematical Economics, 2005, 722-734 Handle: RePEc:hal:journl:halshs-00176476_v1
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