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Optimal Liquidation with Signals: the General Propagator Case

Author

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  • Eduardo Abi Jaber

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Eyal Neuman

    (Imperial College London)

Abstract

We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as minimization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary $L^2$-valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel.

Suggested Citation

  • Eduardo Abi Jaber & Eyal Neuman, 2025. "Optimal Liquidation with Signals: the General Propagator Case," Post-Print hal-03835948, HAL.
    • Handle: RePEc:hal:journl:hal-03835948
    Note: View the original document on HAL open archive server: https://hal.science/hal-03835948v2
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    References listed on IDEAS

    as
    1. Eduardo Abi Jaber & Enzo Miller & Huy^en Pham, 2020. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Papers 2006.13539, arXiv.org, revised Jan 2021.
    2. Alexander Lipton & Umberto Pesavento & Michael G Sotiropoulos, 2013. "Trade arrival dynamics and quote imbalance in a limit order book," Papers 1312.0514, arXiv.org.
    3. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    4. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2014. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88.
    5. Paulwin Graewe & Ulrich Horst, 2016. "Optimal Trade Execution with Instantaneous Price Impact and Stochastic Resilience," Papers 1611.03435, arXiv.org, revised Jul 2017.
    6. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    7. Claudio Bellani & Damiano Brigo & Alex Done & Eyal Neuman, 2021. "Optimal trading: The importance of being adaptive," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 1-18, December.
    8. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    9. Eyal Neuman & Moritz Voß, 2023. "Trading with the crowd," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 548-617, July.
    10. Eyal Neuman & Moritz Vo{ss}, 2021. "Trading with the Crowd," Papers 2106.09267, arXiv.org, revised Mar 2023.
    11. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Post-Print hal-02877569, HAL.
    12. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    13. Eduardo Abi Jaber & Enzo Miller & Huyen Pham, 2021. "Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems," Post-Print hal-03264893, HAL.
    14. Eduardo Abi Jaber & Enzo Miller & Huyen Pham, 2021. "Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03264893, HAL.
    15. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    16. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Post-Print hal-02367200, HAL.
    17. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    18. Eyal Neuman & Alexander Schied, 2016. "Optimal portfolio liquidation in target zone models and catalytic superprocesses," Finance and Stochastics, Springer, vol. 20(2), pages 495-509, April.
    19. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Post-Print hal-02946146, HAL.
    20. Martin Forde & Leandro Sánchez-Betancourt & Benjamin Smith, 2022. "Optimal trade execution for Gaussian signals with power-law resilience," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 585-596, March.
    21. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
    22. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02877569, HAL.
    23. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02367200, HAL.
    24. Eyal Neuman & Moritz Vo{ss}, 2020. "Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact," Papers 2002.09549, arXiv.org, revised Jan 2022.
    25. Eduardo Abi Jaber, 2022. "The Laplace transform of the integrated Volterra Wishart process," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 309-348, January.
    26. Christopher Lorenz & Alexander Schied, 2012. "Drift dependence of optimal trade execution strategies under transient price impact," Papers 1204.2716, arXiv.org, revised Mar 2013.
    27. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02946146, HAL.
    28. Eduardo Abi Jaber, 2020. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Papers 2009.10972, arXiv.org, revised May 2022.
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