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

Bruno Bouchard (), Grégoire Loeper and Xiaolu Tan
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Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, PSL - Université Paris Sciences et Lettres
Grégoire Loeper: Monash University [Melbourne]
Xiaolu Tan: CUHK - The Chinese University of Hong Kong [Hong Kong]

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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 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.

Date: 2022-06
Note: View the original document on HAL open archive server: https://hal.science/hal-03105342v1
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Published in Stochastic Processes and their Applications, 2022, 148, pp.299-323. ⟨10.1016/j.spa.2022.02.010⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03105342

DOI: 10.1016/j.spa.2022.02.010

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