Portfolio Selection Models Under Uncertian Variables

Portfolio selection is to select a combination of securities among a large number of candidate securities which is the best to meet the investors’ goal. In recent years, with the introduction of uncertain theory and credibility theory, many scholars began to employ them to study portfolio selection problems. Numerous models containing fuzzy variable or uncertain variable are proposed. In this paper, we do some research based on uncertain theory and credibility theory as follows:1. Portfolio selection models based on distance between fuzzy variables are studied. The distance between fuzzy variables is used to measure the divergence of fuzzy investment return from a prior one. Two new mathematical models are proposed by expressing divergence as distance, investment return as expected value and risk as variance and semivariance, respectively. Finally, several numerical examples are given to illustrate the effectiveness of the proposed approach.2. Credibilistic portfolio selection models are studied with different investor risk attitudes. By expressing the investment return as expected value and risk as variance, semivariance and chance of bad outcome respectively, we propose three credibilistic portfolio selection models that focus on different investor risk attitudes so that the optimal portfolios for investors who possess different risk attitudes can be achieved more easily.3. Mean-target semivariance diversification model are studied for portfolio selection with uncertain returns. The target semivariance is introduced for uncertain variable, and further a mean-target semivariance diversification model is proposed for uncertain portfolio selection. In addition, a hybrid intelligent algorithm is designed for solving the proposed model. Finally, the numerical results show that the proposed models are efficient.