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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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    1. Stefan Ankirchner & Steffen Dereich & Peter Imkeller, 2005. "The Shannon information of filtrations and the additional logarithmic utility of insiders," Papers math/0503013, arXiv.org, revised May 2006.
    2. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    3. Younes Kchia & Philip Protter, 2015. "Progressive Filtration Expansions Via A Process, With Applications To Insider Trading," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-48.
    4. A. Galichon & P. Henry-Labord`ere & N. Touzi, 2014. "A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options," Papers 1401.3921, arXiv.org.
    5. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    6. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    7. Florens, Jean-Pierre & Fougere, Denis, 1996. "Noncausality in Continuous Time," Econometrica, Econometric Society, vol. 64(5), pages 1195-1212, September.
    8. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Citations

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    Cited by:

    1. Reda Chhaibi & Ibrahim Ekren & Eunjung Noh & Lu Vy, 2022. "A unified approach to informed trading via Monge-Kantorovich duality," Papers 2210.17384, arXiv.org.
    2. 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.
    3. Bingyan Han, 2022. "Distributionally robust risk evaluation with a causality constraint and structural information," Papers 2203.10571, arXiv.org, revised Jun 2025.
    4. 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, November.
    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. Julio Backhoff-Veraguas & Xin Zhang, 2023. "Dynamic Cournot-Nash equilibrium: the non-potential case," Mathematics and Financial Economics, Springer, volume 17, number 1, November.

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