SIAM Journal on Financial Mathematics, Volume 11, Issue 2, Page 593-619, January 2020.
This paper investigates a deep-learning solution to high-dimensional multiperiod portfolio optimization problems with bounding constraints on the control. We propose a deep neural network (DNN) architecture to describe the underlying control process. The DNN consists of $K$ subnetworks, where $K$ is the total number of decision steps. The feedback control function is determined solely by the network parameters. In this way, the multiperiod portfolio optimization problem is linked to a training problem of the DNN, that can be efficiently computed by the standard optimization techniques for network training. We offer a sufficient condition for the algorithm to converge for a general utility function and general asset return dynamics including serially dependent returns. Specifically, under the condition that the global minimum of the DNN training problem is attained, we prove that the algorithm converges with the quadratic utility function when the risky asset returns jointly follow multivariate autoregressive (1) models and/or multivariate generalized autoregressive conditional heteroskedasticity (1,1) models. Numerical examples demonstrate the superior performance of the DNN algorithm in various return dynamics for a high-dimensional portfolio (up to 100 dimensions).

中文翻译：

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具有连续依赖回报的投资组合选择的深度学习解决方案

SIAM金融数学杂志，第11卷，第2期，第593-619页，2020年1月。
本文研究了在控制上有约束的高维多期限投资组合优化问题的深度学习解决方案。我们提出了一种深度神经网络（DNN）架构来描述基础控制过程。DNN由$ K $子网组成，其中$ K $是决策步骤的总数。反馈控制功能仅由网络参数确定。这样，多期投资组合优化问题与DNN的训练问题相关联，可以通过用于网络训练的标准优化技术有效地计算DNN的训练问题。我们为算法收敛到通用效用函数和通用资产收益动态（包括与序列相关的收益）提供了充分的条件。特别，在达到DNN训练问题的全局最小值的条件下，我们证明了当风险资产共同遵循多元自回归（1）模型和/或多元广义自回归条件异方差（1， 1）型号。数值示例说明了DNN算法在高维组合（最多100个维）的各种返回动力学中的优越性能。