Implementing Arrow-Debreu Equilibria by Trading Infinitely-Lived Securities

Abstract

We show that Arrow-Debreu equilibria with countably additive prices in infinite-time economy under uncertainty can be implemented by trading infinitely-lived securities in complete sequential markets under two different portfolio feasibility constraints: Wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement Arrow-Debreu equilibria, while those with price bubbles implement Arrow-Debreu equilibria with transfers. Transfers are equal to price bubbles on initial portfolio holdings. Price bubbles arise in sequential equilibrium under the wealth constraint if some securities are in zero supply or negative prices are permitted, but cannot arise with essentially bounded portfolios.

Keywords: Arrow-Debreu Equilibrium, Security Markets Equilibrium Price Bubbles, Transfers

JEL Classification: D50, G12, E44