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1、ArbitrageTheoryinContinuousTimeSecondEditionOXFORDUNIVERSITYPRESSLJPREFACETOTHESECONDEDITIONOneofthemainideasbehindthefirsteditionofthisbookwastoprovideareasonablyhonestintroductiontoarbitragetheorywithoutgoingintoabstractmeasureandintegrationtheory.Thisapproach,however,hadso
2、mecleardraw-backs:sometopics,likethechangeofnumerairetheoryandtherecentlydevelopedLIBORandswapmarketmodels,areveryhardtodiscusswithoutusingthelanguageofmeasuretheory,andanimportantconceptlikethatofamartingalemeasurecanbefullyunderstoodonlywithinameasuretheoreticframework.,For
3、thesecondeditionIhavethereforedecidedtoincludesomemoreadvancedmaterial,but,inordertokeepthebookaccessibleforthereaderwhodoesnotwanttostudymeasuretheory,Ihaveorganizedthetextasfollows:Themoreadvancedpartsofthebookaremarkedwithastar*.1'Themainpartsofthebookarevirtuallyunchanged
4、andkeptonanelementarylevel(i.e.notmarkedwithastar).fThereaderwhoislookingforanelementarytreatmentcansimplyskip1'thestarredchaptersandsections.Thenonstarredsectionsthusconstituteaself-containedcourseonarbitragetheory.Theorganizationandcontentsofthenewpartsareasfollows:Ihaveadd
5、edappendicesonmeasuretheory,probabilitytheory,andmar-tingaletheory.Theseappendicescanbeusedforalightheartedbuthonestintroductorycourseonthecorrespondingtopics,andtheydefinethepre-requisitesfortheadvancedpartsofthemaintext.Intheappendicesthereisanemphasisonbuildingintuitionfor
6、basicconcepts,suchasmeasur-ability,conditionalexpectation,andmeasurechanges.Mostresultsaregivenformalproofsbutforsomeresultsthereaderisreferredtotheliterature.8Thereisanewchapteronthemartingaleapproachtoarbitragetheory,wherewediscuss(insomedetail)theFirstandSecondFundamentalT
7、he-oremsofmathematicalfinance,i.e.theconnectionsbetweenabsenceofarbitrage,theexistenceofmartingalemeasures,andcompletenessofthemarket.ThefullproofsoftheseresultsareverytechnicalbutIhavetriedtoprovideafairlydetailedguidedtourthroughthetheory,includingtheDelbaen-Schachermayerpr
8、oofoftheFirstFundamentalTheorem.rFollowingthechapteronthegeneralmart
