具有现实约束的均值-下半方差模糊投资组合优化研究

Research on Lower Semi-variance Fuzzy Portfolio Strategy with Real Constraints

在实际投资中,不确定性和现实约束影响着投资决策。为了度量实际投资中的不确定性,本文引入模糊变量,并采用下半方差度量投资组合的风险,考虑一个具有上下界限制、交易成本以及无风险资产借贷约束的均值-下半方差模糊投资组合模型。该模型是一个具有不等式约束的二次规划问题,使用不等式的旋转算法对该模型进行求解。最后,通过“滚动样本”方法,对上述模型与最小方差模型以及等比例模型进行对比与评价。结果表明,本文考虑的模型的夏普比率表现更优。

In order to measure the existing uncertainty in portfolio management,fuzzy variables are used to capture the uncertain returns of different securities in this paper.Therefore,this paper considers a lower semi-variance fuzzy portfolio model that takes into account threshold constraints,transaction cost and borrowing constraints.In the above model,the probabilistic standard semivariance is used to measure the risk.The model is a quadratic programming problem with inequality constraints,which is solved by the pivoting algorithm.Finally,based on a“rolling-sample”approach,the out-of-sample performance of the above model is compared with the minimum variance model and the isometric model.The result indicates the best comparative performance for the proposed model.