Using Dupire’s notion of vertical derivative, we provide a functional (path-dependent) extension of the Itô’s 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.

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