Huesmann, M. (2016). The geometry of multi-marginal Skorokhod embedding. In M. Gordina, T. Kumaga, L. Saloff-Coste, & K.-T. Sturm (Eds.), Heat Kernels, Stochastic Processes and Functional Inequalities (pp. 3096–3099). European Mathematical Society - EMS - Publishing House GmbH. http://hdl.handle.net/20.500.12708/41529
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Book Title:
Heat Kernels, Stochastic Processes and Functional Inequalities
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Abstract:
The martingale optimal transport problem (MOT) is a variant of the optimal transport problem where the coupling is required to be a martingale between its marginals. In dimension one, this problem is well understood for two marginals corresponding to one- step martingales. Via the Dambis-Dubins-Schwarz Theorem the MOT can be translated into a Skorokhod embedding problem (SEP). It turns out that the recently established transport approach to SEP allows for a systematic treatment of all known solutions to (one-dimensional) MOT. We show that the transport approach to SEP extends to a multi-marginal setup. This allows us to show that all known one-marginal solutions have natural multi-marginal coun- terparts. In particular (among other things), we can systematically construct solutions to genuine multi-marginal martingale optimal transport problems. This is joint work with M.Beiglböck and A.Cox
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Keywords:
General Earth and Planetary Sciences; General Environmental Science; Mathematics Subject Classification (2010): 31; 60; 35; 58; 46; 58J65; 53C23; 60F17; 60J45; 35B27.
