A Multi-period Fuzzy Portfolio Optimization Model with Short Selling Constraints

Short selling is one of the important financial vehicles for real investment activities. Most of the traditional fuzzy portfolio models are established without short selling, which cannot effectively guide investors to make profits when stock prices tend to fall. This paper aims to address the multi-period portfolio problem with short selling under fuzzy environment. To comprehensively consider the effect of short selling on the investment process, we propose three types of short selling constraints, i.e., total short selling proportion constraint, short selling cardinality constraint, and lower and upper bound constraint. Then, we establish a multi-period possibilistic mean-semi-variance portfolio selection model with multiple short selling constraints. Next, we design a multiple particle swarm optimization with simulated annealing to solve it. Finally, we illustrate the feasibility and effectiveness of the proposed model and algorithm via a numerical example using actual stock data. The results show that short selling has a significant impact on investment decisions, and our proposed model can help investors construct portfolio strategies with short selling to improve their investment return.