Itô's formula for non-anticipative functionals of càdlàg rough paths

Primavera Francesca, University of Vienna
Cuchiero Christa , University of Vienna
Guo XIn, UC Berkeley

Relying on the approximation properties of the signature of càdlàg rough paths, we derive a (rough) functional Itô's formula for non-anticipative path functionals via a density approach. Our results lead to a functional extension of the classical Itô's formula for rough paths which furthermore coincides with the functional change of variable formula formulated by Cont and Fournié (2010), whenever the relative notions of integration coincide. As a byproduct, we show that sufficiently regular non-anticipative path functionals admit a functional Taylor expansion, leading to a far-reaching extension of the recently established results of Dupire and Tissot-Daguette (2022). This talk is based on ongoing joint work with Christa Cuchiero and Xin Guo.

Area: CS42 - Rough paths and data science (Christian Bayer, Paul Hager and Sebastian Riedel)

Keywords: Càdlàg rough paths, Itô's formula, signature

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