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1、MathematicalFinance,8(4):325-347,1998.On-LinePortfolioSelectionUsingMultiplicativeUpdatesDavidP.HelmboldRobertE.SchapireComputerandInformationSciencesAT&TLabsUniversityofCalifornia180ParkAvenue,RoomA279SantaCruz,CA95064FlorhamPark,NJ07932dph@cse.ucsc.eduschapire@rese
2、arch.att.comYoramSingerManfredK.WarmuthAT&TLabsComputerandInformationSciences180ParkAvenue,RoomA277UniversityofCaliforniaFlorhamPark,NJ07932SantaCruz,CA95064singer@research.att.commanfred@cse.ucsc.eduAbstractWepresentanon-lineinvestmentalgorithmwhichachievesalmostthe
3、samewealthasthebestconstant-rebalancedportfoliodeterminedinhindsightfromtheactualmarketoutcomes.ThealgorithmemploysamultiplicativeupdaterulederivedusingaframeworkintroducedbyKivinenandWarmuth.Ouralgorithmisverysimpletoimplementandrequiresonlyconstantstorageandcomputi
4、ngtimeperstockineachtradingperiod.WetestedtheperformanceofouralgorithmonrealstockdatafromtheNewYorkStockExchangeaccumulatedduringa22-yearperiod.Onthisdata,ouralgorithmclearlyoutperformsthebestsinglestockaswellasCover'suniversalportfolioselectionalgorithm.Wealsopresen
5、tresultsforthesituationinwhichtheinvestorhasaccesstoadditionalsideinformation."1IntroductionWepresentanon-lineinvestmentalgorithmwhichachievesalmostthesamewealthasthebestconstant-rebalancedportfolioinvestmentstrategy.Thealgorithmemploysamultiplicativeupdaterulederiv
6、edusingaframeworkintroducedbyKivinenandWarmuth[20].Ouralgorithmisverysimpletoimplementanditstimeandstoragerequirementsgrowlinearlyinthenumberofstocks.ExperimentsonrealNewYorkStockExchangedataindicatethatouralgorithmoutperformsCover's[9]universalportfolioalgorithm.The
7、followingsimpleexampledemonstratesthepowerofconstant-rebalancedportfoliostrate-gies.Assumethattwoinvestmentsareavailable.The rstisarisk-free,no-growthinvestmentstockwhosevalueneverchanges.Thesecondinvestmentisahypotheticalhighlyvolatilestock.Onevendays,thevalueofthis
8、stockdoublesandonodddaysitsvalueishalved.Therelativereturnsofthe rststockcanbedescribedbythesequence1;1;1;:::andofthesecondbythe11s
