基于贝叶斯理论的可容许均值-方差投资组合优化研究  

The Admissible M-V Portfolio Optimization Based on Bayesian Theory

作　　者：张鹏 林晓妮 ZHANG Peng;LIN Xiao-ni(School of Economics and Management,South China Normal University,Guangzhou 510006,China)

机构地区：[1]华南师范大学经济与管理学院,广东广州510006

出　　处：《数理统计与管理》2024年第3期527-540,共14页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(71271161);广东省自然科学基金项目(2024A1515011808)。

摘　　要：传统M-V模型基于历史数据对预期收益和方差的估计存在不确定性,Bayes理论可以减少模型在参数估计上存在的不足。考虑可容许偏差、投资者的主观情绪偏好、交易成本、借贷约束等现实约束,本文构建基于贝叶斯理论的可容许均值-方差投资组合模型,并运用Bayes理论对模型的参数进行调整。该模型是凸规划问题,本文结合序列二次规划和不等式组旋转算法求解。在样本内,本文计算出不同乐观系数下的最优投资者组合的有效前沿并进行分析。在样本外,文章通过“滚动样本”的方法,将模型的夏普比率与等比例投资组合模型进行比较研究,验证了本文模型的投资效果。The traditional M-V model based on historical data has uncertainty in the estimation of expected return and variance.The shortcomings of the model in parameter estimation can be reduced by Bayes theory.Considering the realistic constraints such as admissible deviation,investor's subjective emotional preference,transaction cost and borrowing constraints,the admissible mean variance portfolio model based on Bayesian theory is constructed in this paper,and Bayesian theory is used to adjust the parameters of the model.These models are convex programming problems,which can be solved by sequential quadratic programming and inequality rotation algorithm.In the sample,the effective frontier of the optimal portfolio under different optimistic indexs are calculated and analyzed in this paper.Outside the sample,this paper uses the method of"rolling sample"to compare the Sharpe ratio of the models with the equal proportion portfolio model,and verifies the investment effect of the models.

关 键 词：可容许M-V投资组合模型 Bayes理论 乐观系数 共轭先验分布 扩散先验分布 

分 类 号：O212[理学—概率论与数理统计]