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Optimal execution and price manipulations in time-varying limit order books

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  • Aur\'elien Alfonsi

    (CERMICS)

  • Jos\'e Infante Acevedo

    (CERMICS)

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    Abstract

    This paper focuses on an extension of the Limit Order Book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied. Here, the additional feature allows a time-varying LOB depth. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude Price Manipulations in the sense of Huberman and Stanzl or Transaction-Triggered Price Manipulations (see Alfonsi, Schied and Slynko). These conditions give interesting qualitative insights on how market makers may create or not price manipulations.

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    File URL: http://arxiv.org/pdf/1204.2736
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1204.2736.

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    Date of creation: Apr 2012
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    Handle: RePEc:arx:papers:1204.2736

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    Web page: http://arxiv.org/

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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. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    3. Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
    4. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    5. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, Springer, vol. 8(3), pages 311-341, 08.
    6. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print, HAL hal-00397652, HAL.
    7. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, Elsevier, vol. 1(1), pages 1-50, April.
    8. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    9. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, Econometric Society, vol. 72(4), pages 1247-1275, 07.
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