随机模糊的等比例-最小方差投资组合优化研究

Markowitz的均值-方差模型在投资组合优化中得到了广泛的运用和拓展,其中多数拓展模型仅局限于对随机投资组合或模糊投资组合的研究,而忽略了实际问题同时包含了随机信息和模糊信息两个方面。本文首先定义随机模糊变量的方差用以度量投资组合的风险,提出具有阀值约束的最小方差随机模糊投资组合模型,基于随机模糊理论,将该模型转化为具有线性等式和不等式约束的凸二次规划问题。为了提高上述模型的有效性,本文以投资者期望效用最大化为压缩目标对投资组合权重进行压缩,构建等比例-最小方差混合的随机模糊投资组合模型,并求解该模型的最优解。最后,运用滚动实际数据的方法,比较上述两个模型的夏普比率以验证其有效性。

Random Fuzzy Mixture of Equally Weighted and Minimum-variance Portfolios Selection Problem

Markowitz’s mean-variance model has been widely used and extended in portfolio optimization. Most of the extended models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical portfolio problems often involve the mixture of the stochastic returns with fuzzy information. In this paper, we first define the variance of random fuzzy variable and then employ it as risk measure. A new minimum variance random fuzzy portfolio selection model with threshold constraints is proposed. Based on random fuzzy theories, the model is transformed into a convex quadratic programming problem with linear equalities and linear inequalities constraints. To improve the performance of the proposed model, we consider mixture of equally weighted and minimum-variance portfolios obtained by shrinking the portfolio weights directly with the target of maximizing the expected utility of investors, and then find the optimal solution. Finally, based on a "rolling-sample" approach, we evaluate the Sharp ratio of the proposed models with empirical dataset to illustrate the validity of the models.