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.
"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