Francesca Primavera

Abstract

We derive a functional Itô-formula for non-anticipative maps of rough paths, based on the approximation properties of the signature of càdlàg rough paths. This result is a functional extension of the Itô-formula for càdlàg rough paths (by Friz and Zhang (2018)), which coincides with the change of variable formula formulated by Dupire (2009) whenever the functionals' representations, the notions of regularity, and the integration concepts can be matched. Unlike these previous works, we treat the vertical (jump) perturbation via the Marcus transformation, which allows for incorporating path functionals where the second order vertical derivatives do not commute, as is the case for typical signature functionals. As a byproduct, we show that sufficiently regular non-anticipative maps admit a functional Taylor expansion in terms of the path's signature, leading to an important generalization of the recent results by Dupire and Tissot-Daguette (2022).

Our speaker

Francesca Primavera is a Postdoctoral Researcher in the Department of Industrial Engineering and Operations Research (IEOR) at the University of California, Berkeley. She earned her PhD in Mathematics from the University of Vienna, where she was advised by Prof. Christa Cuchiero and Dr. Sara Svaluto-Ferro. Her research focuses on stochastic analysis, rough path theory, and mathematical finance, with a particular interest in the mathematical foundations of signature methods and their applications to financial modelling and control problems.

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