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arXiv · 1609.02349

A superhedging approach to stochastic integration

Rafał M. Łochowski·Nicolas Perkowski·David J. Prömel
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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.

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Rafał M. Łochowski, Nicolas Perkowski, David J. Prömel. 2016-09-08. A superhedging approach to stochastic integration. https://arxiv.org/abs/1609.02349

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