Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - RTG1845

Abstract "Optimal transport along martingales"


The problem of finding an optimal transport plan between two probability densities (or measures) goes back to Monge and Kantorovich and has found renewed interest in the last years due to the books of Cedric Villani. It turns out that enhancing the classical problem with martingale constraints (i.e. the transport has to follow a martingale) leads to many interesting new aspects. The enhanced problem exhibits connections to classical probability theory (Skorokhod embeddings) to optimal stochastic control and has important applications to mathematical finance (model independent hedging, robust bounds for prices of exotic options). It has even lead to improvements of classical results like Doob's L^p-inequality. Mathias Beiglböck is a leading researcher in the area of optimal transport and has recently completed, together with Nicolas Julliet, a pathbreaking description of the mathematical foundations of optimal transport with martingale constraints.