A new uncertain random portfolio optimization model for complex systems with downside risks and diversification

There are different types of securities yields in the financial market. The yields of these securities can be described as uncertain variables or random variables. This paper considers an uncertain random portfolio selection prob-lem, in which uncertain and random return rates exist simultaneously. First, by considering downside risks and diversification constraints, an uncertain random bi-objective mean-variance-VaR-entropy model for portfo-lio selection problems is proposed. Here, investment return and risk are, respectively, quantified by uncertain random expected value and variance. Then the formulated uncertain random model is transformed into two equivalent deterministic models. Furthermore, we use the NSGA-II algorithm to solve the equivalent bi-objective model, and propose a new optimal solution criterion to find a single optimal solution in the Pareto op-timal solution set. Finally, a numerical simulation is performed to verify the validity and the practicality of the proposed model and the NSGA-II algorithm. (c) 2022 Elsevier Ltd.

Automated summary

This paper proposes a new portfolio selection model involving uncertain and random return rates. By considering downside risks and diversification constraints, investment return and risk are quantified as uncertain random expected value and variance. The formulated model is transformed into equivalent deterministic models, and the NSGA-II algorithm is used to solve the bi-objective model, with a new optimal solution criterion proposed to find a single optimal solution in the Pareto optimal solution set.