Following a hedging based approach to model free financial mathematics, we prove that it is 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 of finite p-variation for all p> 2. Additionally, we provide various generalizations of F\"ollmer's pathwise It\^o formula.
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-H\"older continuous for all \alpha<1/ 2. Additionally, we provide various generalizations of F\"ollmer's pathwise It\^o formula.
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of finite p-variation for all p>
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