Neural Networks for Portfolio Analysis With Cardinality Constraints

Area of Science:

• Computational Finance
• Machine Learning
• Operations Research

Background:

• The classical Markowitz model for portfolio analysis has limitations in modern finance.
• Transaction costs and cardinality constraints are critical factors not addressed by classical models, especially in high-frequency trading.
• Machine learning tools show promise in solving complex optimization problems.

Purpose of the Study:

• To propose novel dynamic neural network models for nonconvex portfolio optimization.
• To address limitations of classical models by incorporating transaction costs and cardinality constraints.
• To demonstrate the effectiveness of machine learning in financial optimization.

Main Methods:

• Development of three novel dynamic neural networks specifically designed for portfolio optimization.
• Intentionally designing neural dynamics to leverage the problem's structural characteristics.
• Rigorous mathematical proof of global convergence for the proposed models.

Main Results:

• Experimental validation using real stock market data from the Dow Jones Index (DJI) from November 2021 to November 2022.
• Demonstrated efficacy of the proposed dynamic neural network models.
• Achieved a significant reduction in combined investment risk and reward costs by up to 56.71% compared to average portfolio selection.

Conclusions:

• The proposed dynamic neural networks effectively solve nonconvex portfolio optimization problems with transaction costs and cardinality constraints.
• Machine learning offers a powerful approach to overcome limitations of traditional financial models.
• The novel models provide a substantial improvement in portfolio cost reduction and performance.