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Using Dupires notion of vertical derivative, we provide a functional (path-dependent) extension of the It^os formula of Gozzi and Russo (2006) that applies to C^{0,1}-functions of continuous weak Dirichlet processes. It is motivated and illustrated by its applications to the hedging or superhedging problems of path-dependent options in mathematical finance, in particular in the case of model uncertainty
Using rough path theory, we provide a pathwise foundation for stochastic It^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, w
This paper establishes It^os formula along a flow of probability measures associated with gene-ral semimartingales. This generalizes existing results for flow of measures on It^o processes. Our approach is to first prove It^os formula for cylindrical
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and payoff functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics f
A peculiar feature of It^os calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative of semimarti
We derive upper and lower bounds on the expectation of $f(mathbf{S})$ under dependence uncertainty, i.e. when the marginal distributions of the random vector $mathbf{S}=(S_1,dots,S_d)$ are known but their dependence structure is partially unknown. We