Electronic Journal of Probability

Local times for typical price paths and pathwise Tanaka formulas

Nicolas Perkowski and David Prömel

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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.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 46, 15 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H05: Stochastic integrals 60J60: Diffusion processes [See also 58J65]
Secondary: 91G99: None of the above, but in this section

It\^o formula Local times Model uncertainty Tanaka formula

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Perkowski, Nicolas; Prömel, David. Local times for typical price paths and pathwise Tanaka formulas. Electron. J. Probab. 20 (2015), paper no. 46, 15 pp. doi:10.1214/EJP.v20-3534. https://projecteuclid.org/euclid.ejp/1465067152

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