A superhedging approach to stochastic integration

Rafał M. Łochowski, Nicolas Perkowski and David J. Prömel

Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4078-4103

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 càdlàg 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 càdlàg 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.

Keywords: Càdlàg path; Model-independent finance; Quadratic variation; Pathwise stochastic calculus; Stochastic integration; Vovk’s outer measure (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2018.01.009

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