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1、INTRODUCTIONTOSTOCHASTICCALCULUSWITHAPPLICATIONSSECONDEDITIONThispageintentionallyleftblankFimaCKlebanerMonashUniversity,AustraliaImperialCollegePressPublishedbyImperialCollegePress57SheltonStreetCoventGardenLondonWC2H9HEDistributedbyWorldScientificPublishingCo.Pte.Ltd.
2、5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.INTRODUCTIONTOSTOCHASTICCALCULU
3、SWITHAPPLICATIONS(SecondEdition)Copyright©2005byImperialCollegePressAllrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,wi
4、thoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.ISBN1-86094-555-4ISBN1-86094-566-X(
5、pbk)PrintedinSingapore.PrefacePrefacetotheSecondEditionThesecondeditionisrevised,expandedandenhanced.ThisisnowamorecompletetextinStochasticCalculus,frombothatheoreticalandanappli-cationspointofview.Changescameabout,asaresultofusingthisbookforteachingcoursesinStochasticC
6、alculusandFinancialMathematicsoveranumberofyears.Manytopicsareexpandedwithmoreworkedoutexamplesandexercises.Solutionstoselectedexercisesareincluded.Anewchapteronbondsandinterestratescontainsderivationsofthemainpricingmod-els,includingcurrentlyusedmarketmodels(BGM).Thech
7、angeofnumerairetechniqueisdemonstratedoninterestrate,currencyandexoticoptions.ThepresentationofApplicationsinFinanceisnowmorecomprehensiveandself-contained.ThemodelsinBiologyintroducedintheneweditionincludetheage-dependentbranchingprocessandastochasticmodelforcompetitio
8、nofspecies.TheseMarkovprocessesaretreatedbyStochasticCalculustech-niquesusingsomenewrepresentations,suchasarel
