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

Author

Listed:
  • Kühn, Christoph
  • Stroh, Maximilian

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.

Suggested Citation

  • Kühn, Christoph & Stroh, Maximilian, 2013. "Continuous time trading of a small investor in a limit order market," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2011-2053.
  • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2011-2053 DOI: 10.1016/j.spa.2013.01.017
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    References listed on IDEAS

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    8. Martin Šmíd, 2007. "On Uselessness of Limit Orders," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 14(24).
    9. Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997. "Towards a general theory of bond markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 141-174.
    10. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
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