### Multiobjective Particle Swarm Optimization for a Novel Fuzzy Portfolio Selection Problem

Abstract

On the basis of the portfolio selection theory, this paper proposes a novel fuzzy multiobjective model that can evaluate investment risk properly and increase the probability of obtaining an expected return. In building this model, fuzzy value-at-risk (VaR) is used to evaluate the exact future risk in terms of loss. The VaR can directly reflect the greatest loss of a selection case under a given confidence level. Conversely, variance, the measure of the spread of a distribution around its expected value, is utilized to make the selection more stable. This model can provide investors with more significant information for decision making. To solve this model, an improved Pareto-optimal-set-based multiobjective particle swarm optimization (IMOPSO) algorithm is designed to obtain better solutions in the Pareto front. The proposed model and algorithm are exemplified by specific numerical examples. Furthermore, comparisons are made between IMOPSO and other existing approaches. Experiments show that the model and algorithm are effective in solving the multiobjective portfolio selection problem.