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 $α$-Hölder continuous for all $α<1/2$. Additionally, we provide various generalizations of Föllmer's pathwise Itô formula.

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