Modeling of Linear Uncertain Portfolio Selection with Uncertain Constraint and Risk Index

Since securities markets are subject to a great deal of uncertainty and complexity, the returns of securities cannot be accurately estimated by historical data. In this case, it must use experts’ knowledge and judgment. Therefore, we investigate portfolio selection problems in such uncertain environments. First, this paper regards the rate of return on security as an uncertain variable which obeys linear uncertain distribution, and then provides the analytical expressions of the corresponding risk, return and risk index in the uncertain portfolio selection environment. Afterwards, we construct three types uncertain portfolio selection models with uncertain constraint, namely, the minimizing risk, the maximizing return and the maximizing belief degree. Meanwhile, in order to more intuitively reflect the investor’s sense of loss, three types uncertain portfolio selection models considering both uncertain constraint and risk index are also constructed. These models are transformed into corresponding deterministic models. Furthermore, a relevant particle swarm optimization (PSO) algorithm is proposed to solve these models. Finally, through an example analysis, this paper obtains the portfolio selection strategies under different objectives, compares the results under different models, verifies the rationality and effectiveness of the models and algorithm, and analyzes the sensitivity of the parameters