No Free Lunch under Transaction Costs for Continuous Processes

We present a version of the Fundamental Theorem of Asset Pricing and of the Hedging Theorem for security markets under transaction costs for continuous processes. We show that the nflvr condition, which requires that absence of arbitrage is preserved under a smaller bid-ask spread, is equivalent to the existence of a Uniformly Strictly Consistent Price System. We also characterize the superreplication price of bounded contingent claim as the supremum of expected values under all Uniformly Consistent Price Systems.