Martingale Optimal Transport in Robust Finance

Dr. David Prömel, Mannheim Universität


Without assuming any probabilistic price dynamics, we consider a frictionless financial market given by the Skorokhod space, on which some financial options are liquidly traded. In this model-free setting, we show various pricing-hedging dualities and the analogue of the fundamental theorem of asset pricing. For this purpose, we study the corresponding martingale optimal transport (MOT) problem: We obtain a dual representation of the Kantorovich functional (super-replication functional) defined for functions (financial derivatives) on the Skorokhod space using quotient sets (hedging sets). Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional constraints to ensure compatibility with the quotient sets. The talk is based on joint work with Patrick Cheridito, Matti Kiiski and H. Mete Soner.