On the equivalence of financial structures with short-term assets

Two financial structures are equivalent if, for each given state price, the images of their full payoff matrices of these financial structures are equal. The main consequence of this definition is that, regardless of the standard exchange economy Σ, the existence of a financial equilibrium in an exchange economy Σ associated with a financial structure ℱ is equivalent to the existence of an equilibrium in Σ associated with any other financial structure ℱ′ belonging to the equivalence class of ℱ. The main contribution of the paper is to provide a necessary and sufficient condition of equivalence in a multi-period economy if all assets are short-term.