Thumbnail

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

View/Open
Type
Article accepté pour publication ou publié
Date
2022
Journal name
Stochastic Processes and their Applications
Volume
148
Publisher
Elsevier
Pages
299-323
Publication identifier
Metadata
Show full item record
Author(s)
Bouchard, Bruno
CEntre 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 finance