A superhedging approach to stochastic integration

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 c`adl`ag 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 c`adl`ag paths and implies the existence of quadratic variation in the sense of F"ollmer quasi surely under all martingale measures. Based on the robust existence of the quadratic variation, a model-free It^o integration is developed.