Robust Portfolio Selection with GARCH-EVT-Copula

 作者： 陆家涛 作者单位： 1北京理工大学数学与统计学院，北京 刊名： Statistics and Application, 2018, Vol.07 (01), pp.54-64 中文刊名： 统计学与应用, 2018, Vol.07 (01), pp.54-64 来源数据库： Hans Pubs Journal DOI： 10.12677/SA.2018.71008 关键词： CVaR; 中文关键词： CVaR;  GARCH;  EVT;  Copula理论;  鲁棒投资组合; 英文摘要： In this paper, a robust portfolio model is established under the assumption that the underlying distribution is mixed and uncertain. Firstly, we use the GARCH-EVT model to describe the fat tail and heteroscedasticity characteristics of single financial asset return. Then we use Copula to describe the dependence structure between the yields, and establish the GARCH-EVT-Copula model. Finally, a mixture of uncertain multivariate distributions of returns is constructed using different Copula functions, and a robust portfolio model of GARCH-EVT-Copula-WCVaR is estab-lished on the basis of WCVaR-Copula robust model. Compared to the Normal-Copula-WCVaR robust model and the classical mean variance model in the experimental study, the return of GARCH-EVT-Copula-WCVaR robust model is higher than... that of Normal-Copula-WCVaR robust model and mean variance model during the stock market crisis and the period when the volatility of return fluctuates. 中文摘要： 本文在多种金融资产的收益率服从混合不确定多元分布的假设下，建立鲁棒投资组合模型。首先，使用GARCH-EVT模型描述单一金融资产收益率分布的厚尾、异方差特征，然后运用Copula理论描述多个收益率之间的相依结构，建立了描述多种金融资产收益率分布的GARCH-EVT-Copula模型。最后，运用不同的Copula函数构建了收益率的混合不确定多元分布集合，并在WCVaR-Copula鲁棒投资组合模型基础上，建立了GARCH-EVT-Copula-WCVaR鲁棒投资组合模型。通过与经典的均值方差模型、以正态分布刻画边缘分布的Normal-Copula-WCVaR鲁棒模型的实证比较，可以发现，在股价出现极端情况的股灾期间和收益率大幅波动期间，GARCH-EVT-Copula-WCVaR鲁棒模型所建立的投资组合的回报都要高于均值方差模型和Normal-Copula-WCVaR鲁棒模型。