English

A $C^{0,1}$-functional It\^o's formula and its applications in mathematical finance

Probability 2021-01-12 v1 Mathematical Finance

Abstract

Using Dupire's notion of vertical derivative, we provide a functional (path-dependent) extension of the It\^o'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

Keywords

Cite

@article{arxiv.2101.03759,
  title  = {A $C^{0,1}$-functional It\^o's formula and its applications in mathematical finance},
  author = {Bruno Bouchard and Grégoire Loeper and Xiaolu Tan},
  journal= {arXiv preprint arXiv:2101.03759},
  year   = {2021}
}