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Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization

Acciaio, B., Backhoff-Veraguas, J. and Zalashko, A. (2020) Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization. Stochastic Processes and Their Applications, 130 (5). 2918 - 2953. ISSN 0304-4149

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Identification Number: 10.1016/j.spa.2019.08.009

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.

Item Type: Article
Official URL: https://www.journals.elsevier.com/stochastic-proce...
Additional Information: © 2019 Elsevier B.V.
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Date Deposited: 04 Oct 2019 15:09
Last Modified: 06 Sep 2020 23:01
URI: http://eprints.lse.ac.uk/id/eprint/101864

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