Uncertain Entropy as a Risk Measure in Multi-Objective Portfolio Optimization

Subject Areas : Financial Mathematics

Mahsa mahmoodvandgharahshiran ¹ , Gholamhossein Yari ² , Mohammad Hassan Behzadi ³

1 - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Applied Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
3 - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2022-10-25 Accepted : 2023-01-10 Published : 2023-12-01

Keywords: Uncertainty theory, Uncertain Entropy, Multi-Objective Optimization, Information Theory, Uncertain Mean-Entropy Portfolio Optimization (UMEPO),

Abstract :

As we are looking for knowledge of stock future returns in portfolio optimization, we are practically faced with two principal concepts: Uncertainty and Information about variables. This paper attempts to introduce a pragmatic bi-objective investment model based on uncertainty, instead of probability space and information theory, instead of variance and other moments as a risk measure for portfolio optimization. Not only is uncertainty space expected to be more in line with investment theory, but also, applying and learning this approach seems more straightforward and practical for novice investors. The proposed model simultaneously maximizes the uncertain mean of stock returns and minimizes uncertain entropy as a measure of portfolio risk. The uncertain zigzag distribution has been used for variables to avoid the complexity of fitting distributions for data. This uncertain mean-entropy portfolio optimization (UMEPO) has been solved by three meta-heuristic methods of multi-objective optimization: NSGA-II, MOPS, and MOICA. Finally, it was observed that the optimal portfolio obtained from the proposed model has a higher return and a lower entropy as a risk measure compared to the same model in the probability space.

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