Deep-learning solution to portfolio selection with serially-dependent returns

M.Phil.This paper investigates a deep-learning solution to high-dimensional multi-period 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 multi-period 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 AR(1) models and/or multivariate GARCH(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).本文研究有關多時期投資策略優化的問題，尤其當有大量投資資產、投資限制，以及當資產價格走勢呈現前後相關時。我們提供了一個深度學習的解決方法。我們以一個深度神經網路去模擬當中的投資組合價值變化，並將投資策略優化的問題，化作相等的神經網路訓練問題。我們提供了該深度神經網路收斂的充分條件。我們亦證明了: 當該相等的神經網路訓練問題達至最優解，以及價格走勢呈現AR(1) 或是CCCGARCH(1,1) 走勢時，若我們考慮二次元效益曲線，該深度神經網路將收斂。我們於模擬實驗中展示了該深度學習方法能有效處理高維數問題(100 個投資資產)。Tsang, Ka Ho.Thesis M.Phil. Chinese University of Hong Kong 2020.Includes bibliographical references (leaves 27-28).Abstracts also in Chinese.Title from PDF title page (viewed on November 24, 2021)