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General Intensity Shapes in Optimal Liquidation

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  • Olivier Guéant

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study the optimal liquidation problem using limit orders. If the seminal literature on optimal liquidation, rooted to Almgren-Chriss models, tackles the optimal liquidation problem using a trade-off between market impact and price risk, it only answers the general question of the liquidation rhythm. The very question of the actual way to proceed is indeed rarely dealt with since most classical models use market orders only. Our model, that incorporates both price risk and non-execution risk, answers this question using optimal posting of limit orders. The very general framework we propose regarding the shape of the intensity generalizes both the risk-neutral model presented of Bayraktar and Ludkovski and the model developed in Guéant, Lehalle and Fernandez-Tapia, restricted to exponential intensity.

Suggested Citation

  • Olivier Guéant, 2015. "General Intensity Shapes in Optimal Liquidation," Post-Print hal-01393116, HAL.
    • Handle: RePEc:hal:journl:hal-01393116
    DOI: 10.1111/mafi.12052
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    Cited by:

    1. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Sep 2022.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Xiaofei Lu & Fr'ed'eric Abergel, 2018. "Order-book modelling and market making strategies," Papers 1806.05101, arXiv.org.
    4. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    5. Saran Ahuja & George Papanicolaou & Weiluo Ren & Tzu-Wei Yang, 2016. "Limit order trading with a mean reverting reference price," Papers 1607.00454, arXiv.org, revised Nov 2016.
    6. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.

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