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

Author

Listed:
  • Acciaio, B.
  • Backhoff-Veraguas, J.
  • Zalashko, A.

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.

Suggested Citation

  • Acciaio, B. & Backhoff-Veraguas, J. & Zalashko, A., 2020. "Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2918-2953.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:2918-2953
    DOI: 10.1016/j.spa.2019.08.009
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    References listed on IDEAS

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    Cited by:

    1. Julio Backhoff-Veraguas & Daniel Bartl & Mathias Beiglböck & Manu Eder, 2020. "Adapted Wasserstein distances and stability in mathematical finance," Finance and Stochastics, Springer, vol. 24(3), pages 601-632, July.
    2. Bingyan Han, 2022. "Distributionally robust risk evaluation with a causality constraint and structural information," Papers 2203.10571, arXiv.org, revised Jun 2025.
    3. Beatrice Acciaio & Berenice Anne Neumann, 2025. "Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria," Mathematics and Financial Economics, Springer, volume 19, number 3, December.
    4. Reda Chhaibi & Ibrahim Ekren & Eunjung Noh & Lu Vy, 2022. "A unified approach to informed trading via Monge-Kantorovich duality," Papers 2210.17384, arXiv.org.
    5. Mathias Beiglbock & Gudmund Pammer & Lorenz Riess, 2024. "Change of numeraire for weak martingale transport," Papers 2406.07523, arXiv.org.
    6. Daniel Krv{s}ek & Gudmund Pammer, 2024. "General duality and dual attainment for adapted transport," Papers 2401.11958, arXiv.org, revised Nov 2024.
    7. Backhoff-Veraguas, Julio & Källblad, Sigrid & Robinson, Benjamin A., 2025. "Adapted Wasserstein distance between the laws of SDEs," Stochastic Processes and their Applications, Elsevier, vol. 189(C).
    8. Julio Backhoff-Veraguas & Xin Zhang, 2023. "Dynamic Cournot-Nash equilibrium: the non-potential case," Mathematics and Financial Economics, Springer, volume 17, number 1, December.

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