A ℂ^0,1-functional Itô’s formula and its applications in mathematical finance

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. In this context, we also prove a new regularity result for the vertical derivative of candidate solutions to a class of path-depend PDEs, using an approximation argument which seems to be original and of own interest.