Abstract: 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.

Key words: portfolio selection, interval number, interval quadratic programming, interval acceptability degree, transaction costs