Arbitrage and Existence of Equilibrium in Infinite Asset Markets

Abstract

This paper develops a framework for a general equilibrium analysis of asset markets when the number of assets is infinite. Such markets have been studied in financial economics in the context of asset pricing theories. A distinctive feature of an equilibrium model of asset markets is that investors' portfolio-choice sets are typically not bounded below. We prove that an equilibrium exists under a condition that markets are arbitrage-free. The markets are arbitrage-free if there is a price system under which no investor has an arbitrage opportunity. The concept of an arbitrage opportunity used in this paper differs from the standard concept on an arbitrage portfolio in financial markets which is a portfolio that guarantees a non-negative payoff in every event, a positive payoff in some event and has zero price. We provide an extensive discussion of concepts of an arbitrage opportunity.

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