A MODEL-FREE ANALYSIS OF DISCRETE TIME FINANCIAL MARKETS

We discuss fundamental questions of Mathematical Finance such as arbitrage and hedging in the context of a discrete time market with no reference probability. We show how different notions of arbitrage can be studied under the same general framework by specifying a class S of significant sets, and we investigate the richness of the family of martingale measures in relation to the choice of S. We also provide a superhedging duality theorem. We show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and observe how this is related to no-arbitrage considerations. We finally consider the extension of the previous results to markets with frictions.