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November 2016 Pathwise stochastic integrals for model free finance
Nicolas Perkowski, David J. Prömel
Bernoulli 22(4): 2486-2520 (November 2016). DOI: 10.3150/15-BEJ735


We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of Itô’s integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlled rough path integral. We prove that every “typical price path” has a naturally associated Itô rough path, and justify the application of the controlled rough path integral in finance by showing that it is the limit of non-anticipating Riemann sums, a new result in itself. Compared to the first approach, rough paths have the disadvantage of severely restricting the space of integrands, but the advantage of being a Banach space theory.

Both approaches are based entirely on financial arguments and do not require any probabilistic structure.


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Nicolas Perkowski. David J. Prömel. "Pathwise stochastic integrals for model free finance." Bernoulli 22 (4) 2486 - 2520, November 2016.


Received: 1 November 2014; Revised: 1 March 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1346.60078
MathSciNet: MR3498035
Digital Object Identifier: 10.3150/15-BEJ735

Keywords: Föllmer integration , model uncertainty , rough path , stochastic integration , Vovk’s outer measure

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability


Vol.22 • No. 4 • November 2016
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