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Optimal trade execution: A mean quadratic variation approach

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  • Forsyth, P.A.
  • Kennedy, J.S.
  • Tse, S.T.
  • Windcliff, H.
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    Abstract

    We propose the use of a mean quadratic variation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian Motion (GBM) or Arithmetic Brownian Motion (ABM). The exact solution of the ABM formulation is in fact identical to the static (price-independent) approximate solution for the mean–variance objective function in Almgren and Chriss (2000). The optimal trading strategy in the GBM case is in general a function of the asset price. The static strategy determined in the ABM formulation turns out to be an excellent approximation for the GBM case, even when volatility is large.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0165188912001236
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 36 (2012)
    Issue (Month): 12 ()
    Pages: 1971-1991

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    Handle: RePEc:eee:dyncon:v:36:y:2012:i:12:p:1971-1991

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Optimal trading; Mean quadratic variation; HJB equation;

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    References

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    1. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    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.
    3. 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.
    4. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    5. Nikolaus Hautsch & Ruihong Huang, 2009. "The Market Impact of a Limit Order," SFB 649 Discussion Papers SFB649DP2009-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
    7. Basak, Suleyman & Chabakauri, Georgy, 2009. "Dynamic Mean-Variance Asset Allocation," CEPR Discussion Papers 7256, C.E.P.R. Discussion Papers.
    8. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
    9. 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.
    10. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
    11. 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.
    12. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    13. Wang, J. & Forsyth, P.A., 2010. "Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 207-230, February.
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    Cited by:
    1. 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.
    2. 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.

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