Thorpe_KellyCriterion2007

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1、hfalmv.2006/04/07Prn:10/04/2006;10:16F:hfalm1009.tex;VTEX/Juditap.1aid:1009pii:S1872-0978(06)01009-Xdocsubty:REV1Chapter91223THEKELLYCRITERIONINBLACKJACKSPORTSBETTING,3414ANDTHESTOCKMARKET5566EDWARDO.THORP77EdwardO.ThorpandAssociates,NewportBeach,CA92660,USA8899Contents101011Abstract2

2、1112Keywords212131.Introduction313142.Cointossing414153.Optimalgrowth:Kellycriterionformulasforpractitioners815163.1.Theprobabilityofreachingafixedgoalonorbeforentrials816173.2.Theprobabilityofeverbeingreducedtoafractionxofthisinitialbankroll1017183.3.Theprobabilityofbeingatoraboveaspe

3、cifiedvalueattheendofaspecifiednumberof1819trials1119203.4.Continuousapproximationofexpectedtimetoreachagoal1220213.5.Comparingfixedfractionstrategies:theprobabilitythatonestrategyleadsanotheraftern2122trials1222234.Thelongrun:whenwilltheKellystrategy“dominate”?1423245.Blackjack1524256.S

4、portsbetting1725267.Wallstreet:thebiggestgame2126277.1.Continuousapproximation2227287.2.The(almost)realworld2528297.3.Thecasefor“fractionalKelly”2729307.4.Aremarkableformula3030318.Acasestudy3131328.1.Theconstraints3232338.2.Theanalysisandresults3233348.3.Therecommendationandtheresult

5、3334358.4.Thetheoryforaportfolioofsecurities343536363737381Paperpresentedat:The10thInternationalConferenceonGamblingandRiskTaking,Montreal,June1997,3839publishedin:FindingtheEdge:MathematicalAnalysisofCasinoGames,editedbyO.Vancura,J.A.Cor-39nelius,W.R.Eadington,2000.CorrectionsaddedAp

6、ril20,2005.404041HandbookofAssetandLiabilityManagement,Volume141EditedbyS.A.ZeniosandW.Ziemba4242Copyright©2006ElsevierB.V.Allrightsreserved4343DOI:10.1016/S1872-0978(06)01009-Xhfalmv.2006/04/07Prn:10/04/2006;10:16F:hfalm1009.tex;VTEX/Juditap.2aid:1009pii:S1872-0978(06)01009-Xdocsubty

7、:REV2E.O.Thorp19.MyexperiencewiththeKellyapproach351210.Conclusion3623Acknowledgements3634AppendixA.IntegralsforderivingmomentsofE∞3645AppendixB.Derivationofformula(3.1)3756AppendixC.Expectedtimetoreachgoal3967Uncitedreferences4478References44899101011Abstract111212Thecentralproblemfo

8、rgamb