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1、ActaMathematicaScientia2009,29B(6):http://actams.wipm.ac.cnVISCOSITYSOLUTIONSOFHJBEQUATIONSARISINGFROMTHEVALUATIONOFEUROPEANPASSPORTOPTIONS∗BianBaojun( )WangYang()DepartmentofMathematics,TongjiUniversity,Shanghai200092,ChinaZhangJizhou()MathematicsandSciellceCol
2、lege,ShanghaiNormalUniversity,Shanghai200234,ChinaE-mail:zhangjz@shnu.edu.cnAbstractThepassportoptionisacalloptiononthebalanceofatradingaccount.Theoptionholderretainsthegainfromtrading,whiletheissuerisliableforthenetloss.Inthispaper,themathematicalfoundationforpricingt
3、heEuropeanpassportoptionisestablished.Thepricingequationwhichisafullynonlinearequationisderivedusingthedynamicprogrammingprinciple.Thecomparisonprinciple,uniquenessandconvexitypreservingoftheviscositysolutionsofrelatedHJBequationareproved.Arelationshipbetweenthepasspor
4、tandlookbackoptionsisdiscussed.KeywordsPassportoption;HJBequation;viscositysolution;uniqueness;convexitypreserving2000MRSubjectClassification91B02;35B05;49L251IntroductionInthefinancialmarkets,investorstraderiskyassetsforbetterreturns.Aslongastheriskremainssignificant,how
5、ever,aninvestmentintheseassetsdoesnotguaranteeapositivepayoffandinvestorsarepronetobecomevictimsoftheirowntradingstrategies.Avarietyoffinancialderivativesallowtraderstogeneratenon-linearreturnsandhenceenablethemtoavoidextremefinanciallosses.Anexampleofsuchaderivativeisthe
6、passportoption.Thepassportoption,introducedandmarketedbyBankerTrust,isacalloptiononthebalanceofatradingaccount.TheoptionholderisallowedtotradeaparticularassetStduringthelifeoftheoption[0,T].Thenumberofassetsheholdsattimetisdenotedqtandcanbepositive(iftheoptionholderthi
7、nkstheassetpriceisgoingtogoup)ornegative(ifhethinkstheassetpriceisgoingtogodown).Thereisaconstraintonqt:
8、qt
9、≤C.Soqtcanbeany∗ReceivedJanuary8,2007;revisedJanuary20,2008.ResearchofthisworkwassupportedinpartbyNationalScienceFoundationofChina(10371088,10671144),NationalBas
10、icResearchProgramofChina(2007CB814903),DevelopmentFundsofShanghaiHigherEducation(05D210)andtheSpecialFundsforMajorSpe
