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Liquidation In Limit Order Books With Controlled Intensity

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  • Erhan Bayraktar
  • Michael Ludkovski

Abstract

We consider a framework for solving optimal liquidation problems in limit order books. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. We solve this optimal liquidation problem for power-law and exponential-decay order book models and discuss several extensions. We also consider the continuous selling (or fluid) limit when the trading units are ever smaller and the intensity is ever larger. This limit provides an analytical approximation to the value function and the optimal solution. Using techniques from viscosity solutions we show that the discrete state problem and its optimal solution converge to the corresponding quantities in the continuous selling limit uniformly on compacts.
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  • Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
  • Handle: RePEc:bla:mathfi:v:24:y:2014:i:4:p:627-650
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    File URL: http://hdl.handle.net/10.1111/mafi.2014.24.issue-4
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    References listed on IDEAS

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    1. 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.
    2. Erhan Bayraktar & Mike Ludkovski, 2009. "Optimal Trade Execution in Illiquid Markets," Papers 0902.2516, arXiv.org.
    3. 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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