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A superhedging approach to stochastic integration (1609.02349v2)
Published 8 Sep 2016 in q-fin.MF and math.PR
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 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.