A superhedging approach to stochastic integration

Abstract

Using Vovk's outer measure, which corresponds to a minimal superhedging price, the existence of quadratic variation is shown for "typical price paths" in the space of cà dlà g functions possessing a mild restriction on the jumps directed downwards. In particular, this result includes the existence of quadratic variation of "typical price paths" in the space of non-negative cà dlà g paths and implies the existence of quadratic variation in the sense of Föllmer quasi surely under all martingale measures. Based on the robust existence of the quadratic variation, a model-free Itô integration is developed.

25 pages