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

Abstract

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 problem, 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 portfolio 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 optimal solution set. Finally, a numerical simulation is performed to verify the validity and the practicality of the proposed model and the NSGA-II algorithm.