带真实交易条件的投资组合问题研究及实证分析

Research on Portfolio Optimization with Re-al-Life Transaction Restrictions and Empirical Analysis

摘要: 本文研究带真实交易条件的均值–方差模型的理论及实证分析。本文通过引入0-1变量，将含基数约束和半连续变量的均值–方差模型转变为一个标准的混合整数二次规划问题。基于二次凸等价形式的思想，提出了研究模型的一个新的二次凸等价形式。通过求解新等价形式的最优参数来提升原问题的连续松弛下界，从而提升求解分支定界算法的计算效率。最后，本文利用中国的股票沪深300中的个股数据进行数值实验，验证改进的模型对于求解分支定界算法效率提升的效果。

Abstract: In this paper, we study the theory and empirical analysis of mean-variance model with real transaction restrictions. We introduce the 0-1 variable to the semicontinuous variable and transform the model into an integer programming problem. Based on the idea of quadratic convex reformulation, we propose a new quadratic convex reformulation of research model. By solving the optimal parameters of the new reformulation, the lower bound of the continuous relaxation of the original problem is improved, so as to improve the efficiency of the branch and bound algorithm. Finally, this paper analyzes the stock data of China and validates the efficiency.