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Continuous time trading of a small investor in a limit order market

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  • Kühn, Christoph
  • Stroh, Maximilian
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    Abstract

    We provide a mathematical framework to model continuous time trading of a small investor in limit order markets. We show how elementary strategies can be extended in a suitable way to general continuous time strategies containing orders with infinitely many different limit prices. The general limit buy order strategies are predictable processes with values in the set of nonincreasing demand functions. It turns out that our strategy set of limit and market orders is closed, but limit orders can turn into market orders when passing to the limit, and any element can be approximated by a sequence of elementary strategies.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 6 ()
    Pages: 2011-2053

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2011-2053

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    Related research

    Keywords: Limit order markets; Trading strategies; Random measures;

    References

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    1. Guasoni, Paolo & Lépinette-Denis, Emmanuel & Rásonyi, Miklós, 2012. "The fundamental theorem of asset pricing under transaction costs," Economics Papers from University Paris Dauphine 123456789/9300, Paris Dauphine University.
    2. Fabien Guilbaud & Huy�n Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    3. Hugh Luckock, 2003. "A steady-state model of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 385-404.
    4. Luciano Campi & Walter Schachermayer, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Finance and Stochastics, Springer, vol. 10(4), pages 579-596, December.
    5. Martin Šmíd, 2007. "On Uselessness of Limit Orders," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 14(24).
    6. Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
    7. Campi, Luciano & Schachermayer, Walter, 2006. "A super-replication theorem in Kabanov’s model of transaction costs," Economics Papers from University Paris Dauphine 123456789/5455, Paris Dauphine University.
    8. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    9. Martin Šmíd, 2007. "Are Limit Orders Rational?," Acta Oeconomica Pragensia, University of Economics, Prague, vol. 2007(4), pages 32-38.
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