高维协高阶矩的估计及其在投资组合中的应用

The mean-variance portfolio selection techniques can involve a severe welfare loss in the presence of non-quadratic preferences or non-normally distributed asset returns. Thus, the portfolio selection with higher order moments has attracted great attention for many researchers. At present，the research of portfolio selection with higher order moments faces following challenges: the estimation of the higher order moments with high dimensionality is easy fall into “curse of dimensionality” due to so many parameters, the dynamic modeling and estimating of the time-varying higher order moments has just started. Based on the multi-factor model and high frequency data, some efficient estimation methods for the high order moments are given to avoid the “curse of dimensionality” and break the bottleneck for the portfolio selection with higher order moments in his project. We will study the Taylor series expansion of the expected utility function in portfolio selection with higher order co-moments, the static estimation of the multi-factor model and its application in portfolio selection, the dynamic estimation of the time-varying higher order co-moments and its application in portfolio selection and the portfolio selection with higher order co-moments based on high frequency data. We will establish and select the right quantitative model of portfolio selection with higher order co-moments for the real investment markets, give the estimating and testing method for the higher order co-moments matrix, and provide the way to solve the optimization problem and evaluate the economic values of the portfolio selections. This study will further enrich the theoretical and empirical results for the higher order co-moments, provide scientific decision-making basis for the participants in investment and the supervisors in management in the market. It is of important theoretical and practical significance.

资产收益率分布的非正态性或效用函数的非二次性导致均值-方差投资组合面临严重福利损失，基于高阶矩的投资组合研究引起学者们的高度关注。目前，高阶矩估计面临高维协高阶矩矩阵大量参数需要估计易陷入“维数灾难”和时变性高阶矩动态建模估计刚刚起步的挑战。本项目基于多因素模型和高频数据突破高阶矩估计及其在投资组合中所面临的瓶颈，给出有效避免“维数灾难”的协高阶矩估计方法，通过研究协高阶矩投资组合期望效用函数的泰勒级数展开、协高阶矩的静态多因素估计及其在投资组合中的应用、时变性协高阶矩的动态估计及其在投资组合中的应用和基于高频数据的高阶矩投资组合研究，构建和选择适合具体投资市场的高阶矩投资组合数量模型、高阶矩矩阵参数估计与模型检验、投资组合优化求解以及经济价值评价方法。本研究将进一步丰富协高阶矩的理论和经验结果，为市场投资参与者和市场监督管理者提供科学决策依据，具有重要的理论价值和实践意义。

资产收益率分布的非正态性或效用函数的非二次性导致均值-方差投资组合面临严重福利损失，基于高阶矩的投资组合研究引起学者们的高度关注。. 本课题借鉴国际上关于协高阶矩估计和协高阶矩投资组合模型的理论方法和实证结果，运用金融计量经济学、金融经济学、时间序列分析和多元统计分析技术等，以协高阶矩估计和协高阶矩投资组合模型的数量建模、参数估计、模型检验、优化求解与实证分析为主线，通过理论建模与估计方法的创新，结合具体投资市场实际和数据特征，开展了如下几个方面的研究：（1）基于多因素模型给出协高阶矩矩阵的多因素模型估计和最优压缩估计，克服“维数灾难”的影响，研究因素个数的选择与检验、因素模型的稳健估计以及期望效用最大化框架下静态高阶矩的投资组合。（2）研究时变协高阶矩动态模型的建模、识别、估计和评价方法，基于多因素模型研究高维时变协高阶矩的估计，缓解“维数灾难”的影响，在期望效用最大化框架下研究时变性协高阶矩的动态投资组合及经济价值。（3）基于混频数据的高阶矩投资组合建模研究，包括建模、识别、估计和评价等，基于混频多因素模型研究高维时变协高阶矩的估计，缓解“维数灾难”的影响，在期望效用最大化框架下研究混频多因素模型协高阶矩的投资组合及经济价值。（4）基于高频数据的已实现协高阶矩估计研究中、低维度高频协高阶矩的投资组合，比较高、低频数据协高阶矩投资组合策略的经济价值。将高频数据多因素模型和已实现协高阶矩估计相结合以缓解“维数灾难”，在期望效用最大化框架下研究高维度高频协高阶矩的投资组合及经济价值。. 本课题顺利完成预定研究目标，已发表署名本课题资助的期刊论文21篇，其中SCI/SSCI检索学术期刊论文7篇，中文核心期刊14篇；在国际或全国性学术会议作专题报告22次，共培养博士研究生6名、硕士研究生14名。

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