A Mean-Fuzzy Random VaR Portfolio Selection Model in Hybrid Uncertain Environment

This paper aims to study portfolio optimization in hybrid uncertain environment. Different from the existing researches, this paper first presents the definition of fuzzy random Value-at-risk to measure investment risk and uses the lambda-average value of the expected value of the fuzzy random return rate of a portfolio to measure investment return. Then a new mean-fuzzy random VaR portfolio selection model in which return rates of securities are assumed to be fuzzy random variables is proposed. Random simulation technologies are combined together with fuzzy simulation technologies to calculate fuzzy random Value-at-Risk, and a hybrid particle swarm optimization-based hybrid intelligent algorithm is designed to solve the proposed model. Finally, a numerical example is given to illustrate the application of this proposed model. The comparison results between HPSO-HIA and PSO-HIA show that the proposed algorithm-HPSO-HIA is effective for solving the proposed model.