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A $C^{0,1}$-functional Itô's formula and its applications in mathematical finance
Published 11 Jan 2021 in math.PR and q-fin.MF | (2101.03759v1)
Abstract: Using Dupire's notion of vertical derivative, we provide a functional (path-dependent) extension of the It^o'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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