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Application of Genetic Optimization Algorithm in Financial Portfolio Problem.

He Li1, Naiyu Shi1

  • 1School of Sciences, Changzhou Institute of Technology, Changzhou 213000, China.

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This study combines quadratic programming and genetic algorithms for optimal financial portfolio allocation, achieving low risk and high returns. The decomposition method ensures reliable and effective solutions for sparse portfolio problems.

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Area of Science:

  • Computational Finance
  • Optimization Algorithms
  • Investment Management

Background:

  • Traditional portfolio optimization faces challenges with high-dimensional and sparse data.
  • Balancing optimal allocation rates with minimized risk is crucial for investment strategies.
  • Existing algorithms like quadratic programming and genetic algorithms have complementary strengths and weaknesses.

Purpose of the Study:

  • To explore the integration of genetic algorithms and quadratic programming for solving Markowitz's mean-variance model.
  • To apply a decomposition method with penalty functions for nonconvex sparse optimization in financial portfolios.
  • To evaluate the effectiveness of combined algorithmic approaches for financial portfolio optimization.

Main Methods:

  • Implementation of quadratic programming and genetic algorithms using MATLAB.
  • Utilizing genetic algorithm toolboxes for efficient portfolio solutions.
  • Application of the decomposition method of penalty functions for nonconvex sparse optimization.

Main Results:

  • The decomposition method's solutions align with the genetic algorithm's integrated solutions.
  • A specific portfolio allocation example: 67% in local car reserves and 33% in wine reserves.
  • Both quadratic programming and genetic algorithms provide effective portfolio feedback for small data scales.

Conclusions:

  • Combining quadratic programming and genetic algorithms offers a robust approach to financial portfolio optimization.
  • The decomposition method of penalty functions proves reliable and effective for sparse financial portfolio issues.
  • Algorithmic integration enhances the efficiency and accuracy of investment portfolio management.