Arbitrage and equilibrium in economies with infinitely many commodities

An ‘arbitrage opportunity’ for a class of agents is a commodity bundle that will increase the utility of any of the agents and that has non-positive price. The non-existence of ‘arbitrage opportunities’ is necessary and sufficient for the existence of an economic equilibrium. A bundle is ‘priced by arbitrage’ if there is a unique price that it can command without causing an ‘arbitrage opportunity’ to exist. For economies that have infinitely many commodities, appropriate notions of ‘arbitrage opportunities’ and ‘bundles priced by arbitrage’ depend on the continuity of agents’ preferences. This paper develops these notions, thereby providing a foundation for recent work in financial theory concerning arbitrage in continuous-time models of securities markets.