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1、OnHonestTimesinFinancialModelingAshkanNikeghbali1andEckhardPlaten2August1,2018Abstract.Thispaperdemonstratestheusefulnessandimportanceoftheconceptofhonesttimestofinancialmodeling.Itstudiesafinancialmarketwithassetpricesthatfollowjump-diffusionswithnegativejumps.Thecen
2、tralbuildingblockofthemarketmodelisitsgrowthoptimalportfolio(GOP),whichmaximizesthegrowthrateofstrictlypositiveportfolios.Primarysecurityaccountprices,whenexpressedinunitsoftheGOP,turnouttobenonnegativelocalmartingales.Intheproposedframeworkanequivalentriskneutralp
3、robabilitymeasureneednotexist.Derivativepricesareobtainedasconditionalexpectationsofcorrespondingfuturepayoffs,withtheGOPasnumeraireandtherealworldprobabilityaspricingmeasure.Thetimewhentheglobalmaximumofaportfoliowithnopositivejumps,whenexpressedinunitsoftheGOP,isr
4、eached,isshowntobeagenericrepresentationofanhonesttime.Weprovideageneralformulaforthelawofsuchhonesttimesandcomputetheconditionaldistributionsoftheglobalmaximumofaportfoliointhisframework.Moreover,weprovideastochasticintegralrepresentationforuniformlyintegrablemart
5、ingaleswhosearXiv:0808.2892v1[q-fin.CP]21Aug2008terminalvaluesarefunctionsoftheglobalmaximumofaportfolio.Theseformulaearemodelindependentanduniversal.Wealsospecializeourre-sultstosomeexampleswherewehedgeapayoffthatarrivesatanhonesttime.1991MathematicsSubjectClassific
6、ation:primary90A12;secondary60G30,62P20,05C38,15A15.JELClassification:G10,G13Keywordsandphrases:jumpdiffusionmarket,honesttimes,growthoptimalportfolio,benchmarkapproach,realworldpricing,nonnegativelocalmartingales.1Institutf¨urMathematik,Universit¨atZ¨urich,Winterthu
7、rerstrasse190,CH-8057Z¨urich,Switzerland2UniversityofTechnologySydney,SchoolofFinance&EconomicsandDepartmentofMathematicalSciences,POBox123,Broadway,NSW,2007,Australia1IntroductionInthispaperweconsiderageneralclassofjump-diffusionfinancialmarketmodelsunderthebenchmar
8、kapproach,describedinPlaten&Heath(2006).Ourmaingoalis,withinthisframework,toprovidemodelersandinvestorswithextratoolsbasedontheconceptofhonesttim
