Robust Hedging and Pathwise Calculus

We study the connections of two different pathwise hedging approaches. These approaches are Bender-Sottinen-Valkeila (BSV) by Bender et al. (2008, Pricing by hedging and no-arbitrage beyond semimartingales, finance and stochastics, 12(4), pp. 441--468.) and Cont and Fournié (CF) by Cont and Fournié (2010, Change of variable formulas for non-anticipative functionals on path space, Journal of Functional Analysis, 259(4), pp. 1043--1072; in press, Functional Ito calculus and stochastic integral representation of martingales, Annals of probability). We prove that both approaches give the same pathwise hedges, whenever both of the strategies exist. We also prove BSV-type robust replication result for CF strategies.