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Mathematical Problems in Engineering
Volume 2016, Article ID 9461021, 13 pages
Research Article

Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion

Key Laboratory in Machine Learning & Computational Intelligence, College of Mathematics & Information Science, Hebei University, Baoding, Hebei 071002, China

Received 3 December 2015; Accepted 15 February 2016

Academic Editor: Kishin Sadarangani

Copyright © 2016 Ye Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.