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

Bouchard, Bruno; Loeper, Grégoire; Tan, Xiaolu (2021), A C^{0,1} -functional Itô’s formula and its applications in mathematical finance. https://basepub.dauphine.psl.eu/handle/123456789/21733

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Type
Document de travail / Working paper
Lien vers un document non conservé dans cette base
https://hal.archives-ouvertes.fr/hal-03105342
Date
2021
Titre de la collection
Cahier de recherche CEREMADE
Pages
24
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Auteur(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Grégoire
Tan, Xiaolu
Department of Mathematics [CUHK]
Résumé (EN)
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.
Mots-clés
Itô's formula; mathematical finance