Mean-Variance-Entropy Portfolio Selection Models with Uncertain Returns

Diversification portfolio selection problem is an important issue in uncertain economic environment. In this paper, this problem is discussed within the framework of uncertainty theory. First, an uncertain extension mean-variance diversification model is proposed, in which the mean is chosen as the objective function, and variance and proportion entropy as risk and diversity constraints. Then two variations are investigated on the purposes of minimizing the risk and maximizing the diversity measure, respectively. Furthermore, the corresponding analytical mathematical models are deduced via the convenient operational law of uncertain variables. Finally, several numerical examples are given to illustrate the modeling idea. The results showed that the diversification models had higher diversification than the uncertain mean-variance model. The proposed models provide a new method to make decision-making in uncertain portfolio selection problem.