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

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

References in corpus (6)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• Functional Itô calculus and stochastic integral representation of martingales
• On viscosity solutions of path dependent PDEs
• Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
• Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework
• Understanding the dual formulation for the hedging of path-dependent options with price impact

Cited by in corpus (1)

• It{ô}-Dupire's formula for C^{0,1}-functionals of c{à}dl{à}g weak Dirichlet processes