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General Intensity Shapes In Optimal Liquidation

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  • Olivier Guéant
  • Charles-Albert Lehalle

Abstract

The classical literature on optimal liquidation, rooted in Almgren-Chriss models, tackles the optimal liquidation problem using a trade-off between market impact and price risk. Therefore, it only answers the general question of the optimal liquidation rhythm. The very question of the actual way to proceed with liquidation is then rarely dealt with. Our model, that incorporates both price risk and non-execution risk, is an attempt to tackle this question using limit orders. The very general framework we propose to model liquidation generalizes the existing literature on optimal posting of limit orders. We consider a risk-adverse agent whereas the model of Bayraktar and Ludkovski only tackles the case of a risk-neutral one. We consider very general functional forms for the execution process intensity, whereas Gu\'eant et al. is restricted to exponential intensity. Eventually, we link the execution cost function of Almgren-Chriss models to the intensity function in our model, providing then a way to see Almgren-Chriss models as a limit of ours.
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Suggested Citation

  • Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    • Handle: RePEc:bla:mathfi:v:25:y:2015:i:3:p:457-495
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    File URL: http://hdl.handle.net/10.1111/mafi.2015.25.issue-3
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    References listed on IDEAS

    as
    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. 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.
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    6. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
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