Optimal trade execution: A mean quadratic variation approach
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Schied, Alexander & Schoeneborn, Torsten, 2008. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," MPRA Paper 7105, University Library of Munich, Germany.
- 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.
- Carl Chiarella & Giulia Iori & Josep Perello, 2007.
"The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows,"
- Chiarella, C. & Iori, G. & Perello, J., 2008. "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows," Working Papers 08/04, Department of Economics, City University London.
- Carl Chiarella & Giulia Iori, 2005. "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows," Research Paper Series 152, Quantitative Finance Research Centre, University of Technology, Sydney.
- Mike, Szabolcs & Farmer, J. Doyne, 2008.
"An empirical behavioral model of liquidity and volatility,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 32(1), pages 200-234, January.
- Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
- 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.
- 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.
- Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
- 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.
- Nikolaus Hautsch & Ruihong Huang, 2009.
"The Market Impact of a Limit Order,"
SFB 649 Discussion Papers
SFB649DP2009-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Hua He & Harry Mamaysky, 2001.
"Dynamic Trading Policies With Price Impact,"
Yale School of Management Working Papers
ysm244, Yale School of Management, revised 01 Jan 2002.
- Basak, Suleyman & Chabakauri, Georgy, 2009.
"Dynamic Mean-Variance Asset Allocation,"
CEPR Discussion Papers
7256, C.E.P.R. Discussion Papers.
- 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.
- Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:36:y:2012:i:12:p:1971-1991. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.