A ℂ0,1-functional Itô’s formula and its applications in mathematical finance

Bruno Bouchard, Grégoire Loeper and Xiaolu Tan

Stochastic Processes and their Applications, 2022, vol. 148, issue C, 299-323

Abstract: 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 C0,1-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.

Date: 2022
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DOI: 10.1016/j.spa.2022.02.010

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