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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. Paulwin Graewe & Ulrich Horst & Jinniao Qiu, 2013. "A Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions," Science & Finance (CFM) working paper archive 1309.0461, Science & Finance, Capital Fund Management, revised Mar 2014.
    2. 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.
    3. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Science & Finance (CFM) working paper archive 1204.0148, Science & Finance, Capital Fund Management, revised Jun 2013.
    4. Damiano Brigo & Giuseppe Di Graziano, 2013. "Optimal execution comparison across risks and dynamics, with solutions for displaced diffusions," Science & Finance (CFM) working paper archive 1304.2942, Science & Finance, Capital Fund Management, revised May 2014.
    5. Florian Kl\"ock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Science & Finance (CFM) working paper archive 1205.4008, Science & Finance, Capital Fund Management, revised May 2014.
    6. 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.
    7. Theodoros M. Diasakos, 2012. "A Simple Characterization of Dynamic Completeness in Continuous Time," Discussion Paper Series, Department of Economics 201312, Department of Economics, University of St. Andrews, revised 02 Sep 2013.
    8. M. Alessandra Crisafi & Andrea Macrina, 2014. "Optimal Execution in Lit and Dark Pools," Science & Finance (CFM) working paper archive 1405.2023, Science & Finance, Capital Fund Management.
    9. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Science & Finance (CFM) working paper archive 1404.7320, Science & Finance, Capital Fund Management.
    10. Mauricio Labadie & Charles-Albert Lehalle, 2010. "Optimal trading algorithms and selfsimilar processes: a p-variation approach," Working Papers hal-00546145, HAL.
    11. Paulwin Graewe & Ulrich Horst & Eric S\'er\'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Science & Finance (CFM) working paper archive 1309.0474, Science & Finance, Capital Fund Management, revised Dec 2013.
    12. Olivier Gu\'eant, 2012. "Optimal execution and block trade pricing: a general framework," Science & Finance (CFM) working paper archive 1210.6372, Science & Finance, Capital Fund Management, revised Jul 2013.
    13. 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.

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