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Optimal Liquidation with Signals: the General Propagator Case

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  • Eduardo Abi Jaber
  • Eyal Neuman

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, 2022. "Optimal Liquidation with Signals: the General Propagator Case," Papers 2211.00447, arXiv.org.
    • Handle: RePEc:arx:papers:2211.00447
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    References listed on IDEAS

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    1. Charles-Albert Lehalle & Sophie Laruelle (ed.), 2013. "Market Microstructure in Practice," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8967.
    2. 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.
    3. Alexander Lipton & Umberto Pesavento & Michael G Sotiropoulos, 2013. "Trade arrival dynamics and quote imbalance in a limit order book," Papers 1312.0514, arXiv.org.
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    5. 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.
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    9. 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.
    10. 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.
    11. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
    12. 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.
    13. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Post-Print hal-02877569, HAL.
    14. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    15. Eduardo Abi Jaber & Enzo Miller & Huyen Pham, 2021. "Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems," Post-Print hal-03264893, HAL.
    16. Ying Chen & Ulrich Horst & Hoang Hai Tran, 2019. "Portfolio liquidation under transient price impact -- theoretical solution and implementation with 100 NASDAQ stocks," Papers 1912.06426, arXiv.org.
    17. 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.
    18. Aur'elien Alfonsi & Alexander Schied, 2012. "Capacitary measures for completely monotone kernels via singular control," Papers 1201.2756, arXiv.org, revised Feb 2013.
    19. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    20. Eyal Neuman & Moritz Vo{ss}, 2020. "Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact," Papers 2002.09549, arXiv.org, revised Jan 2022.
    21. Christopher Lorenz & Alexander Schied, 2012. "Drift dependence of optimal trade execution strategies under transient price impact," Papers 1204.2716, arXiv.org, revised Mar 2013.
    22. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    23. 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.
    24. 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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    Cited by:

    1. Eduardo Abi Jaber & Eyal Neuman & Moritz Voss, 2023. "Equilibrium in Functional Stochastic Games with Mean-Field Interaction," Working Papers hal-04119787, HAL.
    2. Eyal Neuman & Yufei Zhang, 2023. "Statistical Learning with Sublinear Regret of Propagator Models," Papers 2301.05157, arXiv.org.
    3. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "Optimal liquidation under indirect price impact with propagator," LIDAM Discussion Papers ISBA 2023012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Eduardo Abi Jaber & Eyal Neuman & Moritz Vo{ss}, 2023. "Equilibrium in Functional Stochastic Games with Mean-Field Interaction," Papers 2306.05433, arXiv.org, revised Feb 2024.
    5. Marcel Nutz & Kevin Webster & Long Zhao, 2023. "Unwinding Stochastic Order Flow: When to Warehouse Trades," Papers 2310.14144, arXiv.org.
    6. Natascha Hey & Jean-Philippe Bouchaud & Iacopo Mastromatteo & Johannes Muhle-Karbe & Kevin Webster, 2023. "The Cost of Misspecifying Price Impact," Papers 2306.00599, arXiv.org.

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