Fuzzy-Portfolio-Selection Models With Value-at-Risk

Based on fuzzy value-at-risk (VaR), this paper proposes a new portfolio-selection model (PSM) called the VaR-based fuzzy PSM (VaR-FPSM). Compared with the existing FPSMs, the VaR can directly reflect the greatest loss of a selected case under a given confidence level. In this study, when the security returns are taken as trapezoidal, triangular, and Gaussian fuzzy numbers, several crisp equivalent models of the VaR-FPSM are derived, which can be handled by any linear programming solvers. In general situations, an improved particle swarm optimization algorithm on the basis of fuzzy simulation is designed to search for the approximate optimal solutions. To illustrate the proposed model and the behavior of the improved particle swarm optimization algorithm, two numerical examples are provided, and the results are discussed. Furthermore, the proposed algorithm is compared with some existing approaches to fuzzy portfolio selection, such as the genetic algorithm and simulated annealing.