Fuzzy portfolio selection based on value-at-risk

In this paper, using value-at-risk, a new fuzzy portfolio selection model named VaR-FPSM is proposed. The value-at-risk is the measure of risk, which describes the greatest loss of an investment with some confidence level. When security returns are same kind of fuzzy variable, we derive two crisp equivalent forms of the VaR-FPSM. Furthermore, in general situations, we designed a fuzzy simulation based particle swarm optimization (PSO) algorithm to find an approximately optimal result. To illustrate the proposed model and hybrid PSO algorithm, a numerical example is provided and some discussions on the results are given.