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A convex duality method for optimal liquidation with participation constraints


  • Olivier Gu'eant
  • Jean-Michel Lasry
  • Jiang Pu


In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to approximate the optimal strategy of a trader willing to unwind a large portfolio. The method we propose is very general as it can be applied to multi-asset portfolios with any form of execution costs, including a bid-ask spread component, even when participation constraints are imposed. Our method, based on convex duality, only requires Hamiltonian functions to have $C^{1,1}$ regularity while classical methods require additional regularity and cannot be applied to all cases found in practice.

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  • Olivier Gu'eant & Jean-Michel Lasry & Jiang Pu, 2014. "A convex duality method for optimal liquidation with participation constraints," Papers 1407.4614,, revised Dec 2014.
  • Handle: RePEc:arx:papers:1407.4614

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    References listed on IDEAS

    1. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
    2. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    3. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    4. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279,, revised Jul 2012.
    5. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    6. Tse & Forsyth & Kennedy & Windcliff, 2013. "Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(5), pages 415-449, November.
    7. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    8. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    9. Julian Lorenz & Robert Almgren, 2011. "Mean--Variance Optimal Adaptive Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(5), pages 395-422, January.
    10. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading: Target Close and Implementation Shortfall," Papers 1205.3482,, revised Dec 2013.
    11. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
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