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1、1AssetPriceBubblesinCompleteMarketsRobertA.Jarrow1,PhilipProtter2,andKazuhiroShimbo21JohnsonGraduateSchoolofManagementCornellUniversityIthaca,NY,14850raj15@cornell.edu2SchoolofOperationsResearchandIndustrialEngineeringCollegeofEngineeringCornellUniversityIthaca,NY,14850pep4@cornell.edu,ks266@cor
2、nell.eduSummary.Thispaperreviewsandextendsthemathematical?nanceliteratureonbubblesincompletemarkets.Weprovideanewcharacterizationtheoremforbubblesunderthestandardnoarbitrage(NFLVR)framework,showingthatbubblescanbeofthreetypes.Type1bubblesareuniformlyintegrablemartingales,andthesecanexistwithanin
3、?nitelifetime.Type2bubblesarenon-uniformlyintegrablemartin-gales,andthesecanexistfora?nite,butunbounded,lifetime.Last,type3bubblesarestrictlocalmartingales,andthesecanexistfora?nitelifetimeonly.Whenoneaddsanodominanceassumption(fromMerton[24]),onlytype1bubblesremain.Inaddition,underMerton’snodom
4、inancehypothesis,put-callparityholdsandtherearenobubblesinstandardcallandputoptions.Ouranalysisimpliesthatifonebelievesassetpricebubblesexistandareanimportanteconomicphenomena,thenassetmarketsmustbeincomplete.Keywords:Bubbles;NFLVR;Completemarkets;Localmartingale;Put-callpar-ity;Derivativepricin
5、g1.1IntroductionAlthoughassetpricebubbles,theirexistenceandcharacterization,haveen-thralledtheimaginationofeconomistsformanyyears,onlyrecentlyhasthistopicbeenstudiedusingthetoolsofmathematical?nance,seeinparticularLoewensteinandWillard[22],CoxandHobson[7],JarrowandMadan[20],Gilles[15],GillesandL
6、eroy[16],andHuangandWerner[17].Thepurposeofthispaperistoreviewandtoextendthismathematical?nanceliteratureinordertoincreaseourunderstandingofassetpricebubbles.Inthispaper,2RobertA.Jarrow,PhilipProtter,andKazuhiroShimbowerestrictourattentiontoarbitragefreeeconomiesthatsatisfyboththeno-free-lunch-w
7、ith-vanishing-risk(NFLVR)andcompletemarketshypotheses,inorderthatboththe?rstandsecondfundamentaltheoremsofassetpricingapply.Equivalently,thereexistsauniqueequivalentlocalmartingalemeasure.Weexcludethestudyofincompletemarkets
