Functional Itô formula for fractional Brownian motion

Abstract

We develop the functional Itô/path-dependent calculus with respect to fractional Brownian motion with Hurst parameter $H>\frac{1}{2}$. Firstly, two types of integrals are studied. The first type is Stratonovich integral, and the second type is Wick-Itô integral. Then we establish the functional Itô formulas for fractional Brownian motion, which extend the functional Itô formulas in Dupire (2009) and Cont-Fournié (2013) to the case of non-semimartingale. Finally, as an application, we deal with a class of fractional backward stochastic differential equations (BSDEs). A relation between fractional BSDEs and path-dependent partial differential equations (PDEs) is established.

16 pages

References in corpus (1)

• A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs

Cited by in corpus (1)

• Mean-field backward stochastic differential equations driven by fractional Brownian motion