Policy gradient methods for optimal trade execution in limit order books

Michael Giegrich, Roel Oomen and Christoph Reisinger

Journal of Computational Finance

Abstract: We discuss applications of policy gradient methods for the optimal execution of an asset position via limit orders. We study two examples in-depth: a parametric limit order book (LOB) model and a realistic generative adversarial neural network (GAN) LOB model. In the first case, we apply a zeroth-order gradient estimator to a suitable parameterization of candidate policies and propose modifications to lower the variance in the estimate, including conditional sampling and a backward-in-time recursion. In the second case, we adapt a recently published LOB-GAN model to obtain a differentiable map from the parameters to the objective. We then alter a standard policy gradient method with a pathwise gradient estimator to overcome issues with the nonconvexity and roughness of the loss landscape, studying different initializations using inexact dynamic programming and second-order optimization steps, as well as regularization of the learnt policies. In both cases, we are able to learn effective trading strategies.

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