改进区间可接受度的证券投资组合区间二次规划模型

本文首先基于Markowitz的经典均值方差模型，针对不确定环境下的投资组合问题，把证券的收益率、风险损失率和流动性用区间数描述，建立了一种新的含交易成本的证券投资组合区间二次规划模型。其次，为求解该模型，提出了改进的区间可接受度确定性转换方法，通过引入优化水平α与可接受水平η将不确定二次规划转化为确定型规划。最后，通过数值实验将提出的方法与传统方法进行比较，结果表明本文所提出的方法与模型具有相对较好的可行性与实用性。

Interval Quadratic Programming Model for Portfolio Selection with Improved Interval Acceptability Degree

Based on the Markowitz mean variance model, the portfolio selection problem is disussed under uncertain environment in this paper. Estimation errors or uncertainties in expected return and risk measurement create difficulties for portfolio optimization. A new approach is proposed to treating uncertainty. By using interval numbers to describe the securities return rate, risk loss rate and securities liquidity, the interval analysis is used to extend the classical mean-variance portfolio optimization problem to the cases with bounded uncertainty, and an improved interval quadratic programming model is introduced for portfolio selection by introducing the linear transaction costs and liquidity of securities market. To solve the improved interval quadratic programming model, an effective method based on the improved interval acceptability degree is proposed to transform the uncertain programming into a deterministic programming, which can get effective portfolio's risk range of the model based on the optimization level α and acceptable level η. Thus, based on the portfolio's risk range, investors can choose a reasonable investment plan in an uncertain market environment. In addition, the proposed method is illustrated by three kinds of securities data experiments. The results show that the new approach is better than the method commonly used on portfolio selection. The proposed model provides a new way of investment for investors, and the solution for the model also provides a new idea for the researchers. But in the future, there is still a wide research space for the solution of the interval quadratic programming model for portfolio selection.