Can we learn to beat the best stock

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1、CanWeLearntoBeattheBestStockAllanBorodin1RanEl-Yaniv2VincentGogan1DepartmentofComputerScienceUniversityofToronto1Technion-IsraelInstituteofTechnology2fbor,vincentg@cs.toronto.edurani@cs.technion.ac.ilAbstractAnovelalgorithmforactivelytradingstocksispresented.Whiletradi-tio

2、naluniversalalgorithms(andtechnicaltradingheuristics)attempttopredictwinnersortrends,ourapproachreliesonpredictablestatisticalrelationsbetweenallpairsofstocksinthemarket.Ourempiricalresultsonhistoricalmarketsprovidestrongevidencethatthistypeoftechni-caltradingcan“beatthema

3、rket”andmoreover,canbeatthebeststockinthemarket.Indoingsoweutilizeanewideaforsmoothingcriticalparametersinthecontextofexpertlearning.1Introduction:ThePortfolioSelectionProblemTheportfolioselection(PS)problemisachallengingproblemformachinelearning,onlinealgorithmsand,ofcour

4、se,computationalfinance.Asiswellknown(e.g.seeLugosi[1])sequencepredictionundertheloglossmeasurecanbeviewedasaspecialcaseofportfo-lioselection,andperhapsmoresurprisingly,fromacertainworstcaseminimaxcriterion,portfolioselectionisnotessentiallyanyharder(thanprediction)asshowni

5、n[2](seealso[1],Thm.20&21).Butthereseemstobeaqualitativedifferencebetweenthepracticalutilityof“universal”sequencepredictionanduniversalportfolioselection.Simplystated,universalsequencepredictionalgorithmsundervariousprobabilisticandworst-casemod-elsworkverywellinpracticewh

6、ereastheknownuniversalportfolioselectionalgorithmsdonotseemtoprovideanysubstantialbenefitoveranaiveinvestmentstrategy(seeSec.4).Amajorpragmaticquestioniswhetherornotacomputerprogramcanconsistentlyout-performthemarket.Acloserinspectionoftheinterestingideasdevelopedininformat

7、iontheoryandonlinelearningsuggeststhatapromisingapproachistoexploitthenaturalvolatilityinthemarketandinparticulartobenefitfromsimpleandratherpersistentstatis-ticalrelationsbetweenstocksratherthantotrytopredictstockpricesor“winners”.Wepresentanon-universalportfolioselectiona

8、lgorithm1,whichdoesnottrytopredictwin-ners.Themotivationbehindouralgorithmistherationaleb