A Hybrid Model for Portfolio Optimization: Integrating the Machine Learning and the Cardinality Constrained Mean-Variance Approaches

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

2 Research group for fractional calculus theory and applications, Science and Technology Research Institute, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

3 Centre of Excellence in Mathematics, MHESI, Bangkok, 10400, Thailand

4 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Guilan, Iran

Abstract

This paper focuses on developing an optimal investment portfolio that combines stocks and related options to minimize unsystematic risk. To achieve this goal, we utilize a deep learning algorithm known as the Deep Galerkin Method (DGM), which accurately prices European call and put options within a long-memory stochastic local volatility framework, thereby enhancing pricing accuracy. Using historical data from 79 stocks in the Russell 2000 Index between 2017 and 2022, we apply various machine learning methods—including Random Forest, K-Nearest Neighbors (KNN), and Support Vector Machines (SVM) to identify optimal portfolios suitable for both risk-seeking and risk-averse investors in 2023. To further refine our investment strategy, we integrate the most effective machine learning methods with a Cardinality-Constrained Mean Variance (CCMV) portfolio optimization model. This integration enables us to construct portfolios tailored to different levels of risk tolerance among investors.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 28 May 2026

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