Martingale Optimal Transports in general dimensions and their joint structures
Dr. Tongseok Lim
Mathematical Institute
University of Oxford
Abstract: Martingale Optimal Transport (MOT) problem is a variant of the Optimal Transport problem where the underlying process is assumed to be a martingale. MOT problem was inspired by mathematical finance community who observed the close connection of MOT with the model-independent robust option pricing. Moreover, the dual problem of MOT can be interpreted as finding optimal hedging strategies against liable options.
MOT has been thoroughly studied by many researchers, especially when the underlying asset is real-valued. On the other hand, little has been done for the corresponding vector-valued case which reflects the situation where the option price depends on many assets simultaneously. Since this is often the case in financial markets, it is evident that extension of the existing MOT theory to this multi-assets setting is important. I would like to introduce my research on this previously unexplored field and discuss some open problems.
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