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1、FromStochasticCalculustoMathematicalFinanceYu.KabanovR.LipsterJ.StoyanovFromStochasticCalculustoMathematicalFinanceTheShiryaevFestschriftWith15FiguresABCYuriKabanovRobertLiptserUniversitédeFranche-ComtéDepartmentofElectricalEngineering-Systems16,routedeGrayTel
2、AvivUniversity25030Besan?onCedexP.O.B.39040,RamatAvivFranceTelAviv69978e-mail:youri.kabanov@math.univ-fcomte.frIsraele-mail:liptser@eng.tau.ac.ilJordanStoyanovSchoolofMathematics&StatisticsUniversityofNewcastleNewcastleuponTyneNE17RUUnitedKingdome-mail:jordan.
3、stoyanov@newcastle.ac.ukLibraryofCongressControlNumber:2005938923MathematicsSubjectClassi?cation(2000):60-XX,93-XXISBN-103-540-30782-6SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-30782-2SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsar
4、ereserved,whetherthewholeorpartofthematerialisconcerned,speci?callytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicro?lmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermittedo
5、nlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comcSpring
6、er-VerlagBerlinHeidelberg2006PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspeci?cstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforge
7、neraluse.TypesettingbytheAuthorsandSPIPublisherServicesusingaSpringerLATEXmacropackageCoverart:MargaritaKabanovaCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN:1159122141/3100/SPI543210ToAlbertShiryaevwithlove,admirationandrespectPrefac
8、eThisvolumecontainsacollectionofarticlesdedicatedtoAlbertShiryaevonhis70thbirthday.Themajorityofcontributionsarewrittenbyhisformerstudents,co-authors,colleaguesandadmirersstronglyi
