Optimizing the investment portfolio using the Markowitz model and fuzzy multi-objective programming (case study: Tehran Stock Exchange)

Subject Areas : Industrial Management

Shadi Kanaani ¹ , Mahdi Yousefi Nejad Attari ² , Zohreh Khalilpourshiraz ³

1 - Department of Industrial Engineering, Seraj University, Tabriz, Iran
2 - Department of Industrial Engineering, Bonab Branch, Islamic Azad University, Bonab, Iran
3 - Department of Industrial Engineering, Bonab Branch, Islamic Azad University, Bonab, Iran

Received: 2023-08-21 Accepted : 2023-11-04 Published : 2024-07-27

Keywords: fuzzy planning, optimization, stock portfolio, markovitz model, zimmermann model.,

Abstract :

The stock portfolio optimization model is based on the fact that the future of the company can be predicted and estimated using the company's past data. However, there is no guarantee of the accuracy of this data, as there are many fluctuations in the financial markets. The Markowitz model is based on the selection of the optimal stock to maximize the expected income of the portfolio in determining the share of each stock in the asset portfolio. On the one hand, this model introduces the mathematical expectation of the value of each share in the model. On the other hand, this covariance model considers stock value fluctuations as fixed and exogenous. Therefore, in this research, through Markowitz's theory, a more comprehensive model has been introduced by proposing a new model, which is more efficient than the traditional Markowitz boundary. In this research, multi-objective programming was first used on the issue of stock optimization, and then fuzzy programming was added to it. Risk standard deviation model and Zadeh development theory are among the methods of solving the stock optimization problem in fuzzy state. Also, to solve the problem, the mathematical programming method was used to calculate the upper and lower bounds of the return share. Finally, by explaining the problem and modeling it in Games software, an example of Tehran Stock Exchange has been investigated, which explains the entire investment portfolio optimization model in fuzzy mode.

References:


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