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Itô-Dupire's formula for C^{0,1}-functionals of càdlàg weak Dirichlet processes

Bouchard, Bruno; Vallet, Maximilien (2021), Itô-Dupire's formula for C^{0,1}-functionals of càdlàg weak Dirichlet processes. https://basepub.dauphine.psl.eu/handle/123456789/22569

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-03368703
Date
2021
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
15
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vallet, Maximilien
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We extend to càdlàg weak Dirichlet processes the C^{0,1}-functional Itô-Dupire's formula of Bouchard, Loeper and Tan (2021). In particular, we provide sufficient conditions under which a C^{0,1}-functional transformation of a special weak Dirichlet process remains a special weak Dirichlet process. As opposed to Bandini and Russo (2018) who considered the Markovian setting, our approach is not based on the approximation of the functional by smooth ones, which turns out not to be available in the pathdependent case. We simply use a small-jumps cutting argument.