基于Copula理论的投资组合算法的分析与应用的中期报告摘要：本文主要研究基于Copula理论的投资组合算法，通过对历史数据的统计分析和Copula模型的拟合，构建适用于股票市场的多维投资组合模型。利用此模型可以得到股票之间的相互关系，进而优化投资组合，降低投资风险。本文运用SAS软件进行实证分析，选取了中国股市中6只典型股票，根据历史数据构建出各股票的收益率序列和相关性矩阵，然后对多维Copula模型进行拟合，得到股票之间的Copula函数，最后通过MonteCarlo模拟法进行投资组合优化，得到了不同权重下的最优投资组合。实证结果表明，基于Copula理论的投资组合算法在降低投资风险、提高收益稳定性方面具有重要的应用价值。关键词：Copula理论；投资组合；股票市场；相关性；MonteCarlo模拟Abstract:ThispaperstudiestheinvestmentportfolioalgorithmbasedonCopulatheory.ByanalyzinghistoricaldataandfittingCopulamodels,amulti-dimensionalinvestmentportfoliomodelsuitableforstockmarketsisconstructed.Thismodelcanbeusedtoobtaintherelationshipbetweenstocks,andthenoptimizetheinvestmentportfoliotoreduceinvestmentrisk.Inthispaper,SASsoftwareisusedforempiricalanalysis.SixtypicalstocksintheChinesestockmarketareselected.Accordingtohistoricaldata,theyieldsequenceandcorrelationmatrixofeachstockareconstructed,andthenthemulti-dimensionalCopulamodelisfittedtoobtaintheCopulafunctionofthestocks.Finally,MonteCarlosimulationisusedtooptimizetheinvestmentportfolio,andtheoptimalinvestmentportfoliounderdifferentweightsisobtained.TheempiricalresultsshowthattheinvestmentportfolioalgorithmbasedonCopulatheoryhasimportantapplicationvalueinreducinginvestmentriskandimprovingreturnstability.Keywords:Copulatheory;investmentportfolio;stockmarket;correlation;MonteCarlosimulation