
A C0,1-functional Itô's formula and its applications in mathematical finance
Bouchard, Bruno; Loeper, Gregoire; Tan, Xiaolu (2022), A C0,1-functional Itô's formula and its applications in mathematical finance, Stochastic Processes and their Applications, 148, p. 299-323. 10.1016/j.spa.2022.02.010
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Type
Article accepté pour publication ou publiéDate
2022Journal name
Stochastic Processes and their ApplicationsVolume
148Publisher
Elsevier
Pages
299-323
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Show full item recordAuthor(s)
Bouchard, BrunoCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Loeper, Gregoire
Monash University [Victoria, Australia]
Tan, Xiaolu
The Chinese University of Hong Kong [Hong Kong]
Abstract (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-0,1functions 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.Subjects / Keywords
Itô's formula; mathematical financeRelated items
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