论文标题
关于参数最佳执行和机器学习代理
On Parametric Optimal Execution and Machine Learning Surrogates
论文作者
论文摘要
我们在离散时间内研究最佳订单执行问题，并具有瞬时价格影响和随机弹性。首先，在线性瞬态价格影响的情况下，我们得出了最佳战略的封闭形式递归，从而扩展了Obizhaeva和Wang的确定性结果（J Financial Markets，2013年）。其次，我们根据Bouchaud等人提出的非线性瞬态价格影响的情况，基于动态编程和深度学习开发一种数值算法。 （量化金融，2004年）。具体而言，我们利用了一个参与者批评框架，该框架为价值函数和反馈控制构建了两个神经网络（NN）替代。 NN功能近似器的灵活可伸缩性可实现参数学习，即将几种模型或市场参数作为输入空间的一部分。众所周知，价格影响，弹性等的精确校准非常具有挑战性，因此了解执行策略对这些参数的敏感性至关重要。我们的NN学习者在多个输入维度上有机地缩放，并显示出在广泛的参数配置上准确近似最佳策略。我们提供了一个完全可重现的jupyter笔记本电脑，我们的NN实现具有独立的教学意义，证明了NN替代物在（参数）随机控制问题中的易用性。
We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy, extending the deterministic results from Obizhaeva and Wang (J Financial Markets, 2013). Second, we develop a numerical algorithm based on dynamic programming and deep learning for the case of nonlinear transient price impact as proposed by Bouchaud et al. (Quant. Finance, 2004). Specifically, we utilize an actor-critic framework that constructs two neural-network (NN) surrogates for the value function and the feedback control. The flexible scalability of NN functional approximators enables parametric learning, i.e., incorporating several model or market parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the execution policy to these parameters. Our NN learner organically scales across multiple input dimensions and is shown to accurately approximate optimal strategies across a wide range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.
