Arbitrage and State Price Deflators in a General Intertemporal Framework

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,tau;), endowed with an order structure, if for each closed convex cone C in X such that Csupe;X₋ and Ccap;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}(Omega;,F,P) if (Omega;,F,P) fails to be sigma-finite.Then we prove that the Kreps-Yan theorem is valid for topological vector spaces in separating duality lang;X,Yrang;, provided Y satisfies both a completeness condition and a Lindelouml;f-like condition.We apply this result to the characterization of the no-arbitrage assumption in a general intertemporal framework