Before revision:  For a frictionless market consisting of d risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of an upper semicontinuous path dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures.
After revision:  For a frictionless market consisting of d risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all martingale measures.