Abstract: We rely on the approximation properties of the signature of càdlàg rough paths to derive a functional Itô formula for non-anticipative maps of rough paths. This leads to 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) as well as by Cont and Fournie (2010), whenever the notions of integration coincide. As a byproduct, we show that sufficiently regular non-anticipative path functionals admit a functional Taylor expansion, leading to a wide generalization of the recently established results by Dupire and Tissot-Daguette (2022). The talk is based on ongoing joint work with Xin Guo and Francesca Primavera.

Bio: Christa Cuchiero is professor at the University of Vienna since 2020. She received a Ph.D. in Mathematics from ETH Zurich in 2011
and got her habilitation in Mathematics from the University of Vienna in 2018. She has received several prizes and fellowships,
including the START award of the Austrian Science Fund (FWF). She has given a number of keynote speeches
and serves on the editorial board of several academic journals. She has also co-organised international conferences and two
world online seminar series on “Machine Learning in Finance” and “Women in Data Science and Mathematics”.
Her research interests span from Mathematical Finance and Probability Theory to Machine Learning and Data Science.