具有范数约束的随机模糊最小方差投资组合决策

Norms-constrained Random Fuzzy Minimum-variance Portfolios Selection

基于Markowitz现代投资组合理论,本文首先将证券收益定义为随机模糊变量,用其方差来度量投资组合的风险。在考虑不同交易成本和估计误差存在的情况下,本文提出了具有权重范数约束的最小方差随机模糊投资组合模型,并在其目标函数中引入范数交易成本。基于随机模糊理论,将上述模型转化为具有线性等式和非线性不等式约束的二次规划问题,采用旋转算法进行求解。最后,运用滚动实际数据的方法,比较上述模型的Sharpe Ratio以验证其有效性。

Based on Markowitz’s modern portfolio theory,in this paper,we first define security return as a random fuzzy variable,and use its variance to measure the risk of portfolio.Considering different transaction costs and the existence of estimation errors,we propose weight-norm-constrained random fuzzy minimum variance portfolio model,whose objective function introduces norm transaction costs.According to random fuzzy theories,the model is transformed into a quadratic programming problem with linear equalities and nonlinear inequalities constraints,and then using pivoting algorithm to find the solution.Finally,based on a"rolling empirical data"approach,we compare the Sharp ratio of the proposed models to illustrate the validity of the models.