Abstract
Based on the Markowitz mean variance model, this paper discusses the portfolio selection problem in an uncertain environment. To construct a more realistic and optimized model, in this paper, a new general interval quadratic programming model for portfolio selection is established by introducing the linear transaction costs and liquidity of the securities market. Regarding the estimation for the new model, we propose an effective numerical solution method based on the Lagrange theorem and duality theory, which can obtain the effective upper and lower bounds of the objective function of the model. In addition, the proposed method is illustrated with two examples, and the results show that the proposed method is better and more feasible than the commonly used portfolio selection method.
Highlights
With the mature development of the securities market, in the last decade, studies have paid increasing attention to the theory of portfolio selection
This paper focuses on the Lagrange dual algorithm to solve the general interval quadratic programming model for portfolio selection
The investment proportions are as follows: The lower bound of the objective function: x 1⁄4 ð0:0352; 0:8197; 0:1451Þ; f ðxÞ 1⁄4 0:0181: The upper bound of the objective function: x 1⁄4 ð0:0188; 0:0365; 0:9447Þ; f ðxÞ 1⁄4 0:0537: Combining these results, we conclude that the objective values of this general interval quadratic programming is in the range of f(x) = [0.0181,0.0537]
Summary
With the mature development of the securities market, in the last decade, studies have paid increasing attention to the theory of portfolio selection. Li and Tian (2008) extended Liu and Wang’s method and developed a new algorithm to optimize the upper bounds of the coefficients in the general interval quadratic programming problem with all coefficients in the objective function, and its constraints are interval numbers [34]. Based on a partial-order relation in the set of intervals, Kuamr et al (2013) developed a method to determine an acceptable optimal feasible solution to solve the generalized interval quadratic programming model, and applied to the securities portfolio selection [39]. We develop a new general interval quadratic programming model for portfolio selection by introducing the linear transaction costs and liquidity of the securities market, which makes the model more optimized and closer to the actual situation. For more details on theory of interval numbers, see [42]
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