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Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach

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  • Alexandre Roch

    (University of Quebec at Montreal)

Abstract

We present a learning algorithm based on simulation and neural networks to solve a stochastic optimal control problem with a large state space using dynamic programming. The problem consists in liquidating a given number of shares of a stock through a limit order book (LOB). The state space includes prices and quantities at each level in the LOB. The objective is to maximize the expected liquidation proceeds. Shares are sold by market orders matching the current limit orders in the LOB and have an impact on the future evolution of the LOB. The optimal strategy is obtained using a hybrid form of performance and value iteration procedures based on neural networks. The probability distribution of the LOB is estimated by a deep learning classification task. The model is tested on 12 stocks traded through the NYSE Arcabook, and a numerical implementation shows that the model outperforms the most common optimal liquidation models in the literature by a significant amount.

Suggested Citation

  • Alexandre Roch, 2023. "Optimal Liquidation Through a Limit Order Book: A Neural Network and Simulation Approach," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09996-z
    DOI: 10.1007/s11009-023-09996-z
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    References listed on IDEAS

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