关键词: 投资组合, Yager熵, 基数约束, 逐步宽容法, 粒子群算法

Abstract: Based on the possibility theory, assuming that the future returns of each asset are trapezoidal fuzzy numbers, a mean-variance-Yager entropy model is constructed including V-type transaction costs, upper and lower bounds of investment proportion and cardinal constraints. By adopting Gradual Tolerance Method with tolerance amount, the tri-objective model is transformed into a single-objective model. By adjusting the tolerance amount to control the return and risk, investors can choose their own investment decisions according to their preferences. In addition, this paper describes the search speed by non-linear inertia weight, and proposes an improved particle swarm optimization algorithm by initializing some particles with poor individual optimal fitness, which reduces the possibility of falling into the local optimum. At the same time, the cardinal constraints and upper and lower bounds constraints are processed by 0-1 matrix and a scaling factor, which makes the solution of the model more effective. Finally, an example is given to illustrate the feasibility and effectiveness of the algorithm. The effective frontier of portfolio is given, and the effect of the change of risk/return tolerance amount is analyzed when the return/risk tolerance amount remains unchanged, which furthermore provides more decision-making selections for investors.

Key words: portfolio selection, Yager entropy, cardinal constraints, gradualtolerance method, particle swarm optimization