Neural Networks for Portfolio Analysis With Cardinality Constraints

Portfolio analysis is a crucial subject within modern finance. However, the classical Markowitz model, which was awarded the Nobel Prize in Economics in 1991, faces new challenges in contemporary financial environments. Specifically, it fails to consider transaction costs and cardinality constraints, which have become increasingly critical factors, particularly in the era of high-frequency trading. To address these limitations, this research is motivated by the successful application of machine learning tools in various engineering disciplines. In this work, three novel dynamic neural networks are proposed to tackle nonconvex portfolio optimization under the presence of transaction costs and cardinality constraints. The neural dynamics are intentionally designed to exploit the structural characteristics of the problem, and the proposed models are rigorously proven to achieve global convergence. To validate their effectiveness, experimental analysis is conducted using real stock market data of companies listed in the Dow Jones Index (DJI), covering the period from November 8, 2021 to November 8, 2022, encompassing an entire year. The results demonstrate the efficacy of the proposed methods. Notably, the proposed model achieves a substantial reduction in costs (which combines investment risk and reward) by as much as
$56.71\%$
compared with portfolios that are averagely selected.