基于聚類與RMT過濾的均值-方差改進模型.pdf

1、大連理工大學碩士學位論文基于聚類與RMT過濾的均值方差改進模型姓名：夏冰申請學位級別：碩士專業(yè)：經濟系統分析與管理指導教師：黃飛雪20090601基于聚類和RMT的均值一方差改進模瓔ClusterandRMTforImprovingontheMeanVarianceModelAbstractWeconsidertheproblemofthestaffsticaluncertaintyofthecorrelationmatrixinthe

2、optimizationofafinancialportfolio，andfoellsontheapplicationofclusterandrandommatrixtheory(RMT)inMarkowitz’Sportfoliomodel，wheretheestimationofthecorrelationmatrixisunavoidablyassociatedwithastatisticaluncertaintyduetothe

3、finitelengthoftheassetreturntimeseriesHierarchicalclusteranalysisisfoundthatitisquiterobustwithrespecttomeasurementnoiseduetothefinitenessofsamplesizeSinglelinkagemethodandaveragemethodadoptedherearebothhierarchicalclust

4、eranalysisSingle1inkageclusterisakindofhierarchicalclusteranalysisInthesinglelinkageprocedure，thedistancebetweenclusterPandclusterqisdefinedbythenearestdistancebetweentheelementsinclusterPandtheelementofclusterqAverageli

5、nkageisantherhierarchicalclusteranalysisadoptedhere，whosedistancebetweenclusterPandclusterqisdefinedastheaveragedistanceofallelementsofpandqByusingthehierarchicalclusterprocedurethenumberofdistinctelementsofthecorrelatio

6、ncoe伍cientmatrixturnsfromnfn1)／2ton一1Thenthecorrelationcoef!ficientmatrixisapositiveultrametricmatrixWeconstructtheportfoliobysolvingtheMarkowitzoptimizationproblembyusingtheultrametricmatrixratherthantheoriginalcorrelat

7、ionmatrixTherandommatrixtheory(RMT)takesthestockmarketasacomplexsystem，inwhichtheelementsactoneachotherinunknownwaysItneedsthreest印StouseI蝴Ttofilterthecorrelationcoefficientmatrix：(1)measurethechaoticdegreeofthesystemwit

8、htheoriginalcorrelationcoefficientmatrix；(2)calculatetheeigenvaluesofthechaoticdegree；(3)removethemeaninglesspartoftheeigenvaluesTotesttheeffectofthefilters，weusethedataof2004—2007ofthe50stockscomposingtheSSE50indextocal

9、culatethecorrelationcoef!ficientmatrixandapplythehierarchicalclusteranalysisprocedureandRMTtofilteritBasedonthefilteredmatrixandoriginalmatrix，weusetheMarkowitzportfoliomodelThenwecomparethereliabilityrisk，effectivesizea

10、ndinvestmentbehavioroftheportfoliosandtheresultsareasfollow：(1)TherealizedriskandthepredictriskoftheRMTportfoliosareboththesmallestandtheseoftheaveragelinkageportfoliosarethelargest，andtheseoftheMarkowitz’sportfoliosandt