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An Optimal Execution Problem in the Volume-Dependent Almgren-Chriss Model

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  • Takashi Kato

Abstract

In this study, we introduce an explicit trading-volume process into the Almgren-Chriss model, which is a standard model for optimal execution. We propose a penalization method for deriving a verification theorem for an adaptive optimization problem. We also discuss the optimality of the volume-weighted average-price strategy of a risk-neutral trader. Moreover, we derive a second-order asymptotic expansion of the optimal strategy and verify its accuracy numerically.

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  • Takashi Kato, 2017. "An Optimal Execution Problem in the Volume-Dependent Almgren-Chriss Model," Papers 1701.08972, arXiv.org, revised Aug 2017.
    • Handle: RePEc:arx:papers:1701.08972
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    References listed on IDEAS

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    1. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    2. Alexander Schied, 2012. "Robust Strategies for Optimal Order Execution in the Almgren-Chriss Framework," Papers 1204.2717, arXiv.org, revised May 2013.
    3. Konishi, Hizuru, 2002. "Optimal slice of a VWAP trade," Journal of Financial Markets, Elsevier, vol. 5(2), pages 197-221, April.
    4. Holthausen, Robert W. & Leftwich, Richard W. & Mayers, David, 1987. "The effect of large block transactions on security prices: A cross-sectional analysis," Journal of Financial Economics, Elsevier, vol. 19(2), pages 237-267, December.
    5. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    6. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    7. Olivier Guéant & Royer Guillaume, 2014. "VWAP execution and guaranteed VWAP," Post-Print hal-01393121, HAL.
    8. Olivier Gu'eant & Guillaume Royer, 2013. "VWAP execution and guaranteed VWAP," Papers 1306.2832, arXiv.org, revised May 2014.
    9. Alexander Schied, 2013. "Robust Strategies for Optimal Order Execution in the Almgren--Chriss Framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 264-286, July.
    10. Takashi Kato, 2016. "Optimality of VWAP Execution Strategies under General Shaped Market Impact Functions," Papers 1605.03683, arXiv.org, revised May 2016.
    11. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
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    Cited by:

    1. Takashi Kato, 2017. "An Optimal Execution Problem with S-shaped Market Impact Functions," Papers 1706.09224, arXiv.org, revised Oct 2017.

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