Local times for typical price paths and pathwise Tanaka formulas

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 $\hat{I}\pm$-Hölder continuous for all $\hat{I}\pm <1/2$. Additionally, we provide various generalizations of Föllmer's pathwise Itô formula.