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This study introduces a dynamic programming algorithm for knapsack-based portfolio optimization, ensuring integer share numbers and efficiency for high-priced stocks. It offers a more realistic approach to financial market modeling.

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Area of Science:

  • Finance
  • Operations Research

Background:

  • Portfolio optimization is crucial for financial markets, but existing models often lack realistic assumptions.
  • High-priced stocks and discrete share quantities present unique challenges in portfolio selection.

Purpose of the Study:

  • To develop a more realistic and efficient model for portfolio optimization using a knapsack-based approach.
  • To introduce a novel dynamic programming algorithm for solving this discrete optimization problem.

Main Methods:

  • The study models portfolio optimization as a knapsack problem with discrete variables.
  • A dynamic programming algorithm is proposed to find the optimal integer number of shares.
  • The algorithm's validity is demonstrated through case studies on the US stock exchange.

Main Results:

  • The proposed dynamic programming algorithm efficiently solves the discrete portfolio optimization problem.
  • The model incorporates realistic features like integer share quantities and high-priced stocks.
  • Case studies confirm the algorithm's applicability and effectiveness in US stock exchange data.

Conclusions:

  • Dynamic programming provides an effective method for knapsack-based portfolio optimization with discrete variables.
  • The developed model enhances the realism and efficiency of portfolio selection for high-priced stocks.
  • This approach offers a valuable alternative to existing portfolio optimization methods in financial markets.