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A portfolio selection model based on the knapsack problem under uncertainty.

Fereshteh Vaezi1, Seyed Jafar Sadjadi1, Ahmad Makui1

  • 1Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran.

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This study introduces a new investment planning method for determining the exact number of shares for assets like Berkshire Hathaway. It uses a knapsack model with interval values to overcome limitations of traditional percentage-based allocation methods.

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Area of Science:

  • Finance
  • Operations Research
  • Computer Science

Background:

  • Traditional asset allocation methods often yield impractical fractional share allocations for high-value stocks.
  • Determining the precise number of shares for investment is crucial for practical portfolio management.

Purpose of the Study:

  • To propose a novel portfolio selection model for determining the number of shares for each asset.
  • To address the limitations of traditional methods in handling high-value assets and fractional shares.

Main Methods:

  • A knapsack-based portfolio selection model incorporating interval values for returns, prices, and budget.
  • Extraction of interval weights from an interval comparison matrix to determine share priority.
  • Conversion to a parametric linear programming model with an optimism threshold.
  • Design of a discrete firefly algorithm for optimizing solutions in large-scale problems.

Main Results:

  • The proposed model provides a practical approach to determining the number of shares, overcoming the impracticality of fractional allocations.
  • The interval-based approach effectively handles uncertainty in financial data.
  • The discrete firefly algorithm efficiently finds near-optimal solutions for complex portfolio selection.

Conclusions:

  • The developed knapsack-based model offers a superior alternative to traditional methods for share allocation, especially for high-value assets.
  • The integration of interval values and optimization algorithms enhances the robustness and practicality of investment planning.
  • The study demonstrates a viable computational approach for real-world stock market investment decisions.