Arbitrage and Hedging in Model-Independent Markets with Frictions

Abstract

We provide a fundamental theorem of asset pricing and a superhedging theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the robust no arbitrage condition introduced by Schachermayer in [Math. Finance, 14 (2004), pp. 19--48] and show that this is equivalent to the existence of consistent price systems. Moreover, we prove that the superhedging price for a claim g coincides with the frictionless superhedging price of g for a suitable process in the bid-ask spread.