Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 46, 15 pp.
Local times for typical price paths and pathwise Tanaka formulas
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.
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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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