B0787
Title: Higher rank signatures and filtrations
Authors: Chong Liu - ShanghaiTech University (China) [presenting]
Abstract: Filtration is an abstract and important notion that appears naturally in stochastic analysis, which models the information flow generated by underlying stochastic processes. However, many well-known statistical methods cannot detect filtrations as they are based on weak topology. Consequently, they may lead to significant errors in those circumstances where the evolution of information plays a crucial role. We will introduce a new methodology based on the signature kernel learning approach, which can be used to give a precise description of filtrations hidden behind observed signals. We will then illustrate that this method provides a feasible statistical tool for lots of filtration--sensitive cases; in particular, it allows to reduce highly non--linear path-and-filtration dependent functionals (e.g. the pricing of American option) to a linear regression problem, which reveals an interesting combination of (Hopf) algebra and kernel learning.
