Model-free Ito integration via pathwise super-hedging
Using Vovk’s hedging based approach to mathematical finance, one can determine sample path properties of "typical price paths" belonging to the space of continuous functions or of non-negative càdlàg functions. Interestingly, all results for "typical price paths" hold quasi surely under all martingale measures. We prove that "typical price paths" possess quadratic variation and local limes. This allows us to develop model-free Itô integration as well as pathwise stochastic calculus for local times. This talk is based on joint works with R.M. Lochowski and N. Perkowski.