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

By Beatrice Acciaio, Julio D. Backhoff Veraguas, Anastasiia Zalashko. Stochastic Processes and their Applications, 2016

66 citations recorded by the source corpus.

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. Our results have natural extensions to the case of general multidimensional continuous semimartingales.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/9984d1e4fa69c50fe41649ed4fc3ae8da1922a12

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Citations in the corpus

The Wasserstein space of stochastic processes (2021, background): “A systematic treatment and use of causality as an interesting property of abstract transport plans between filtered probability spaces and their associated optimal transport problems was initiated by Lassalle [53] and Acciaio, Backhoff, and Zalashko [1].”
Martingale Benamou–Brenier: A probabilistic perspective (2017, background): “Let μ := 1/2(λ|[−3,−2] + λ|[2,3]), ν := 1/6(λ|[−4,−1] + λ|[1,4]).”
All adapted topologies are equal (2019, background): “Acciaio, Zalashko, and one of the present authors consider in [2] the adapted Wasserstein distance in continuous time in connection with utility maximization, enlargement of filtrations and optimal stopping.”