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, and consequently they may lead to significant errors for those circumstances where the evolution of information plays a crucial role. In this talk we will introduce a new methodology based on the signature kernel learning approach developed by Terry Lyons which can be used for giving 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.