Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization
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Date
2020-05Type
- Journal Article
ETH Bibliography
yes
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Abstract
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 counterparts of the aforementioned non-adapted mappings. We provide a necessary and sufficient condition for a Brownian motion 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 robust transport-based estimates for the value of having additional information, as well as model sensitivity with respect to the reference measure, for the classical stochastic optimization problems of utility maximization and optimal stopping. Show more
Publication status
publishedExternal links
Journal / series
Stochastic Processes and their ApplicationsVolume
Pages / Article No.
Publisher
ElsevierSubject
Causal transport plan; Semimartingale decomposition; Filtration enlargement; Stochastic optimization; Robust bounds; Value of informationOrganisational unit
09727 - Acciaio, Beatrice / Acciaio, Beatrice
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ETH Bibliography
yes
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