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A. Zalashko, J. Backhoff, M. Beiglböck:
"Causal transport in discrete time and applications";
Talk: VCMF2016 Vienna Congress on Mathematical Finance, Wien; 2016-09-12 - 2016-09-14.

We study the optimal transport under the causal constraint, which introduces the arrow of time into the problem. Loosely speaking, causal transport plans are a relaxation of adapted processes in the same sense as Kantorovich transport plans extend Monge-type transport maps. The corresponding causal version of the transport problem has recently been introduced by R. Lassalle. Working in a discrete time setup, we establish a recursive formulation for the problem that links the causal transport problem to the recently introduced non-linear transport problems by Gozlan et al. (2015). Moreover, the causal analogues to the Brenier maps are identified under precise conditions. A first consequence of this is the application of strengthened transport-information inequalities in the context of stochastic optimization, complementing the works of Pflug et al. (2009-2012), that serve to gauge the discrepancy between stochastic programs driven by different noise distributions. Finally, the developed techniques give a new light into some classical problems in Mathematical Finance, for which the time-information structure is central, as enlargement of filtrations and optimal stopping.

This is joint work with Julio Backhoff, Mathias Beiglböck and Yiqing Lin.

https://fam.tuwien.ac.at/events/vcmf2016/VCMF2016_conference.pdf