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

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 invest-ment 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 in-vestment theory, but also, applying and learning this approach seems more straightforward and practical for novice investors. The proposed model simulta-neously 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, MOPSO, 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 com-pared to the same model in the probability space.