Abstract
Due to the complexity of financial markets, there exist situations where security returns and background factor returns are available mainly based on experts’ subjective beliefs, such as in the case of lack of historical data. To deal with such indeterminate quantities, uncertain variables are introduced. Based on uncertainty theory, this paper discusses the distribution function of the optimal portfolio return. Two types of new uncertain programming models, namely, the chance-mean model and the measure-mean model, are proposed to make an optimal portfolio selection decision in an uncertain environment. It is proved that there exists an equivalent relation between the chance-mean model and a deterministic linear programming model, which leads to an approach to obtain the optimal solutions of the proposed models. Finally, some numerical examples are illustrated to show the modelling ideas and the effectiveness of the models.
Highlights
Portfolio selection involves creating a combination of securities to maximize portfolio return and spread risk
Uncertainty theory is a powerful technique to deal with belief degrees. erefore, this paper introduces two novel portfolio selection models based on uncertainty theory
(2) In contrast with the existing uncertain portfolio selection models, this paper proposes two novel uncertain portfolio selection models, in which the borrowing constraint and background risk are considered simultaneously
Summary
Portfolio selection involves creating a combination of securities to maximize portfolio return and spread risk. Within the framework of fuzzy set theory, the portfolio selection decision problem has been widely studied. Huang and Qiao [45] discussed the multiperiod portfolio selection problem and proposed a risk index model. Enterprises may have more choices among more potential projects In this vein, this paper will consider a portfolio selection problem within the framework of uncertainty theory with a borrowing constraint.
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