Uncertain bi-objective portfolio programming models of risky assets with liquidity and entropy constraints under uncertainty theory based DEA efficiency measures

Abstract

Portfolio optimization is an important class of decision management problems. In addition, data envelopment analysis method is often used to evaluate the pros and cons of the portfolio. In this paper, we propose a bi-objective portfolio model based on uncertainty theory, and present an uncertain Banker–Charnes–Cooper-data envelopment analysis (BCC-DEA) model to evaluate uncertain portfolios of risky assets. Firstly, we propose an uncertain bi-objective portfolio model with liquidity and entropy constraints. Among them, the risk index is selected as the risk measure which considers the risk-free interest rate. Then, through the different uncertainty distributions of uncertain variables, the uncertain bi-objective portfolio model is transformed into different crisp forms. Furthermore, we construct an uncertain BCC-DEA model to evaluate the uncertain bi-objective portfolio model. Finally, some numerical simulations are given to illustrate the effectiveness and practicality of the presented uncertain bi-objective portfolio model and BCC-DEA model based on the bi-objective genetic algorithm.