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B. Acciaio, J. Backhoff, A. Zalashko:
"Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization";
mathpubs.com, November 09 (2016), 1 - 29.

The martingale part in the semimartingale decomposition of a Brownian
motion with respect to an enlargement of its filtration, is an anticipative mapping of the given Brownian motion. In analogy to optimal transport theory, we define causal transport plans in the
context of enlargement of filtrations, as the Kantorovich counte
rparts of the aforementioned non-adapted mappings. We provide a necessary and sufficient condition for a Brownian mo-
tion to remain a semimartingale in an enlarged filtration, in terms of certain minimization problems over sets of causal transport plans. The latter are also used in order to give an estimate of the value of having additional information, for some classical stochastic optimiza-
tion problems. Our results have natural extensions to the case of
general multidimensional continuous semimartingales.

Causal transport plan; Semimartingale decomposition Filtration en largement Stochastic optimization Value of information Duality

http://www.mathpubs.com/search/category/Mathematics+-+Optimization+and+Control