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Description

Transport (MOT) and its links with probability theory and mathematical finance as well as some of its optimal transport heritage. From an OT perspective, MOT is a version the classical OT problem with a further constraint that the transport plan is a martingale. From a probabilistic perspective, thinking in continuous time, it is the problem of selection a solution to the Skorokhod embedding problem with an additional optimality property. Finally, from a financial perspective, it is the problem of computing range of no-arbitrage prices (primal) and robust hedging strategies which enforce these (dual), when given market quoted prices for co-maturing vanilla options (calls). MOT offers an exciting interaction of the three fields. It brought tremendous new geometrical insights into structure of (optimal) Skorokhod embeddings and it links naturally with martingale inequalities. In exchange, probabilistic methods offer explicit transport plans and the problem, when compared with OT, features an intricate structure of polar sets. In this talk we endeavour to present a panorama of the field with emphasis on some recent contributions.