paper
A $C^{0,1}$-functional Itô's formula and its applications in mathematical finance
Bruno Bouchard, Grégoire Loeper, Xiaolu Tan
A $C^{0,1}$-functional Itô's formula and its applications in mathematical finance
Bruno Bouchard, Grégoire Loeper, Xiaolu Tan
paper2021-01-11English
quantitative financearxiv
Description
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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