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2015 Local times for typical price paths and pathwise Tanaka formulas
Nicolas Perkowski, David Prömel
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Electron. J. Probab. 20: 1-15 (2015). DOI: 10.1214/EJP.v20-3534

Abstract

Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is $\alpha$-Hölder continuous for all $\alpha < 1/2$. Additionally, we provide various generalizations of Föllmer's pathwise Itô formula.

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Nicolas Perkowski. David Prömel. "Local times for typical price paths and pathwise Tanaka formulas." Electron. J. Probab. 20 1 - 15, 2015. https://doi.org/10.1214/EJP.v20-3534

Information

Accepted: 18 April 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1321.60152
MathSciNet: MR3339866
Digital Object Identifier: 10.1214/EJP.v20-3534

Subjects:
Primary: 60H05, 60J60
Secondary: 91G99

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