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Adaptive Execution: Exploration and Learning of Price Impact

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  • Beomsoo Park
  • Benjamin Van Roy

Abstract

We consider a model in which a trader aims to maximize expected risk-adjusted profit while trading a single security. In our model, each price change is a linear combination of observed factors, impact resulting from the trader's current and prior activity, and unpredictable random effects. The trader must learn coefficients of a price impact model while trading. We propose a new method for simultaneous execution and learning - the confidence-triggered regularized adaptive certainty equivalent (CTRACE) policy - and establish a poly-logarithmic finite-time expected regret bound. This bound implies that CTRACE is efficient in the sense that the ({\epsilon},{\delta})-convergence time is bounded by a polynomial function of 1/{\epsilon} and log(1/{\delta}) with high probability. In addition, we demonstrate via Monte Carlo simulation that CTRACE outperforms the certainty equivalent policy and a recently proposed reinforcement learning algorithm that is designed to explore efficiently in linear-quadratic control problems.

Suggested Citation

  • Beomsoo Park & Benjamin Van Roy, 2012. "Adaptive Execution: Exploration and Learning of Price Impact," Papers 1207.6423, arXiv.org.
  • Handle: RePEc:arx:papers:1207.6423
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    1. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    2. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    3. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    4. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
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