具有交易成本的组合投资优化模型及其算法

The emphasis of our research is on portfolio selection models and their algorithms including the standard mean-variance model, the mean-variance model under convex transaction costs, the mean-variance model under convex loan costs, the mean-absolute deviation model and so on. We developed a pivoting based method to solve mean-variance portfolio selection models which has two fundamental forms, one is called full pivoting method and another one is called inverse matrix method. The former requires about about n2 multiplications and additions for each iterations and the latter is linear in n. We conducted tests by using 70 weekly data of 1072 stocks from Shanghai and Shenzhen stock markets of China which indicate that our algorithm is faster not only than Simplex algorithm for solving the same scale linear programming but also than Gausian elimination method for solving the same scale system of linear equations even by the full pivoting method.

本项目研究组合投资中的优化模型与算法。重点研究具有交易成本和特殊约束的组合证券优化模型（一般为混合整数规划）与投资组合更新问题及其计算方法。利用本人提出的投影算法编制计算程序进行较大规模实证分析以验证模型的适用性和算法的有效性。本研究有助于提高管理学科定量分析及计算技术之水平，促进证券操作的理性行为和投资运作的规范化。..