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Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework

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  • JIM GATHERAL

    ()
    (Department of Mathematics, Baruch College, CUNY, One Bernard Baruch Way, New York, NY 10010, USA)

  • ALEXANDER SCHIED

    ()
    (Department of Mathematics, University of Mannheim, A5, 6, 68131 Mannheim, Germany)

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    Abstract

    With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren–Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 14 (2011)
    Issue (Month): 03 ()
    Pages: 353-368

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:03:p:353-368

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    Related research

    Keywords: HJB; optimal execution; risk measures; market impact;

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    Cited by:
    1. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.
    2. Damiano Brigo & Giuseppe Di Graziano, 2013. "Optimal execution comparison across risks and dynamics, with solutions for displaced diffusions," Papers 1304.2942, arXiv.org, revised May 2014.
    3. Paulwin Graewe & Ulrich Horst & Eric S\'er\'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Dec 2013.
    4. Somayeh Moazeni & Thomas Coleman & Yuying Li, 2013. "Regularized robust optimization: the optimal portfolio execution case," Computational Optimization and Applications, Springer, vol. 55(2), pages 341-377, June.
    5. 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.
    6. Florian Kl\"ock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Papers 1205.4008, arXiv.org, revised May 2014.
    7. Olivier Gu\'eant, 2012. "Optimal execution and block trade pricing: a general framework," Papers 1210.6372, arXiv.org, revised Jul 2014.
    8. Theodoros M. Diasakos, 2011. "A Simple Characterization of Dynamic Completeness in Continuous Time," Carlo Alberto Notebooks 211, Collegio Carlo Alberto.
    9. Paulwin Graewe & Ulrich Horst & Jinniao Qiu, 2013. "A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions," Papers 1309.0461, arXiv.org, revised Mar 2014.
    10. Mauricio Labadie & Charles-Albert Lehalle, 2010. "Optimal trading algorithms and selfsimilar processes: a p-variation approach," Working Papers hal-00546145, HAL.
    11. R. Cesari & M. Marzo & P. Zagaglia, 2012. "Effective Trade Execution," Working Papers wp836, Dipartimento Scienze Economiche, Universita' di Bologna.
    12. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
    13. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320, arXiv.org.
    14. M. Alessandra Crisafi & Andrea Macrina, 2014. "Optimal Execution in Lit and Dark Pools," Papers 1405.2023, arXiv.org.

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