Pathwise stochastic integrals for model free finance
By Nicolas Perkowski, David J. Promel. 2013
75 citations recorded by the source corpus.
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o'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 It\^o 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.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/7467814cebaf179c83eb64fc2eca68d685cc3265
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In Finance
- Peter K. Friz
- Huilin Zhang
- Terry Lyons
- Ben M. Hambly
- Guy Flint
- Nicolas Victoir
- Samy Tindel
- Massimiliano Gubinelli
In Management Science and Operations Research
Citations in the corpus
- Differential equations driven by rough paths with jumps (2017, background): “As such, they may constitute natural mathematical tools in the field of robust finance [37].”
- Discretely sampled signals and the rough Hoff process (2013, background): “We note in passing that an alternative pathwise integral in the context of mathematical finance via rough path theory can be found in the preprint [24] (the authors thank the referee for pointing out this paper).”