Abstract

In this talk I will briefly overview some recent theoretical advances for this topic in the last five years, such as the seminal works by M. Beiglboeck et. al. which established the foundations of so–called bicausal optimal transport for stochastic processes, as well as a recent contribution by H. Oberhauser et.al. which applied the signature methods from rough path theory to detect the distances between stochastic processes in adapted topologies. We will also discuss how to use these adapted topologies to solve some practical problems in mathematical finance.