基于非凸交易成本的投资组合优化问题求解

摘要

为使模型更加贴近现实投资场景,从而使投资组合进一步有效指导投资实践,对均值-绝对差(MAD)模型进行扩展,引入分段线性非凸交易成本函数,加入阈值和基数约束等条件,允许卖空,建立多条件约束下的非凸MAD模型.在此基础上选取与标准普尔500指数、罗素2000、罗素3000指数相关的数据集,使用IBM CPLEX进行模型求解和并行分析,将结果与交易成本函数为线性的模型进行对比,对比结果表明,在相同风险水平下,该模型具有更高的收益率和较好的可扩展性.%To make the model more close to reality,and make the portfolio guide the investment practice more effectively,in addition to the introduction of the transaction costs which was depicted by piecewise linear nonconvex function,the basic mean-absolute deviation (MAD) model was extended,constraints such as threshold constraints and cardinality constraints were added into the model,and one was allowed to sell assets short.The multi-constrained non-convex MAD model which was closer to real investment scenario was established.Data sets corresponding to the S&P 500 index,the Russell 2000 index and the Russell 3000 index respectively were used with the help of IBM CPLEX to solve the problem and to do the parallel analysis.The comparison results with the model whese transaction costs is depicted by linear function show that under the same level of risk,the rate of the return of the nonconvex model is significantly higher and the model has good scalability.