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Cardinality-constrained portfolio selection based on collaborative neurodynamic optimization.

Man-Fai Leung1, Jun Wang2

  • 1School of Science and Technology, Hong Kong Metropolitan University, Kowloon, Hong Kong.

Neural Networks : the Official Journal of the International Neural Network Society
|November 4, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel collaborative neurodynamic optimization approach for cardinality-constrained portfolio selection. This method effectively balances investment risk and return while managing transaction costs for investors.

Keywords:
Cardinality constraintMixed-integer programmingNeurodynamic optimizationPortfolio selection

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Area of Science:

  • Quantitative Finance
  • Computational Finance
  • Operations Research

Background:

  • Portfolio optimization is crucial for financial markets, with cardinality constraints being vital for investors to minimize transaction costs and avoid odd lots.
  • Existing methods often struggle to efficiently handle the complexity introduced by cardinality constraints in portfolio selection.
  • High-frequency traders particularly benefit from strategies that incorporate these constraints for practical execution.

Purpose of the Study:

  • To present a collaborative neurodynamic optimization approach for solving the cardinality-constrained portfolio selection problem.
  • To formulate the problem as a mixed-integer optimization problem solvable by the proposed neurodynamic method.
  • To enhance the distribution of Pareto-optimal solutions through iterative weight optimization.

Main Methods:

  • Scalarization of Markowitz's expected return and risk into a weighted Chebyshev function.
  • Equivalency representation of cardinality constraints using binary variables.
  • Application of collaborative neurodynamic optimization employing recurrent neural networks and particle swarm optimization (PSO).
  • Iterative refinement of Pareto-optimal solutions by optimizing weights via PSO.

Main Results:

  • The collaborative neurodynamic approach effectively solves cardinality-constrained portfolio optimization problems.
  • Experimental results demonstrate superior performance compared to existing exact and metaheuristic methods.
  • The method successfully handles the trade-off between investment risk, expected return, and cardinality constraints.

Conclusions:

  • The proposed collaborative neurodynamic optimization is a powerful and efficient method for cardinality-constrained portfolio selection.
  • This approach offers practical advantages for investors, especially high-frequency traders, by managing costs and optimizing portfolios.
  • The study validates the effectiveness of integrating recurrent neural networks with PSO for complex financial optimization tasks.