不允许卖空的含参数均值–方差投资组合模型

Parameterized Mean-Variance Investment Portfolio Model with No Short Sale

摘要: 为了描述投资组合问题的动态变化性，本文提出了一类含参数均值–方差投资组合模型。与类似模型相比，该模型具有以下特点：均值与协方差是时间的函数；考虑了噪声与计算误差等因素的影响；资源不允许卖空，即其要求决策变量非负。针对该模型，本文给出了一类抗噪声在线求解算法。理论分析表明，对于各类噪声，该在线算法生成的误差是有界的，并且该上界随时间的增长快速趋于零。最后，初步的仿真实验验证了所设计算法的有效性。

Abstract: In order to describe the dynamic change of investment portfolio problem, this paper proposes a kind of portfolio model with parameter mean-variance. Compared with similar models, this model has the following characteristics: The mean and covariance contain a time parameter; the influence of noise and calculation error is considered; short selling of resources is not allowed, that is, it requires non-negative decision variables. For this model, a class of anti-noise online algorithm is presented in this paper. Theoretical analysis shows that the error generated by the online algorithm is bounded for all kinds of noises, and the upper bound quickly approaches zero with the increase of time. Finally, a preliminary simulation experiment verifies the effectiveness of the proposed algorithm.