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Article Dans Une Revue Stochastic Processes and their Applications Année : 2022

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

Résumé

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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Dates et versions

hal-03105342 , version 1 (11-01-2021)

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Bruno Bouchard, Grégoire Loeper, Xiaolu Tan. A C^{0,1}-functional Itô's formula and its applications in mathematical finance. Stochastic Processes and their Applications, 2022, 148, pp.299-323. ⟨10.1016/j.spa.2022.02.010⟩. ⟨hal-03105342⟩
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