A superhedging approach to stochastic integration

Rafa{\l} M. {\L}ochowski, Nicolas Perkowski and David J. Pr\"omel

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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.

Date: 2016-09, Revised 2017-09
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Citations: View citations in EconPapers (1)

Published in Stoch. Process. Appl., Vol. 128, No. 12, p. 4078-4103, 2018

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