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On Bellman equation in the limit order optimization problem for high-frequency trading

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  • M. I. Balakaeva
  • A. Yu. Veretennikov

Abstract

An approximation method for construction of optimal strategies in the bid \& ask limit order book in the high-frequency trading (HFT) is studied. The basis is the article by M. Avellaneda \& S. Stoikov 2008, in which certain seemingly serious gaps have been found; in the present paper they are carefully corrected. However, a bit surprisingly, our corrections do not change the main answer in the cited paper, so that, in fact, the gaps turn out to be unimportant. An explanation of this effect is offered.

Suggested Citation

  • M. I. Balakaeva & A. Yu. Veretennikov, 2025. "On Bellman equation in the limit order optimization problem for high-frequency trading," Papers 2510.15988, arXiv.org.
    • Handle: RePEc:arx:papers:2510.15988
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    References listed on IDEAS

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    1. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    2. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
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