个人简介
许明宇，女，1978年1月26日出生，副高级。
2000年毕业于山东大学，获学士学位
2005年获山东大学理学博士学位与法国UniversiteduMaine博士学位
2006-2008年，复旦大学博士后研究
2008年，中国科学院数学与系统科学研究院助理研究员
现任中国科学院数学与系统科学研究院副研究员
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Superhedgingunderratioconstraint.
Weconsidersuperhedgingofcontingentclaimsunderratioconstraint.Ithasbeenwidelyrecognizedthattheminimumcostofsuperhedgingacontingentclaimwithcertainportfolioconstraintsisequaltothepriceofaclaimwithappropriatelymodifiedpayoffbutwithoutconstraints.Intermsofthebackwardstochasticdifferentialequation(BSDE)andthevariationalinequalityequationapproach,werevisitthisresultandprovidetwocounterexamples.
Numericalalgorithmsandsimulationsforreflectedbackwardstochasticdifferentialequationswithtwocontinuousbarriers.
Inthispaperwestudydifferentalgorithmsforreflectedbackwardstochasticdifferentialequations(BSDEinshort)withtwocontinuousbarriersbasedontheframeworkofusingabinomialtreetosimulate1-dBrownianmotion.Weintroducenumericalalgorithmsbythepenalizationmethodandthereflectedmethod,respectively.Intheendsimulationresultsarealsopresented.
Thetimefractionalheatconductionequationinthegeneralorthogonalcurvilinearcoordinateandthecylindricalcoordinatesystems.
InthispaperatimefractionalFourierlawisobtainedfromfractionalcalculus.AccordingtothefractionalFourierlaw,afractionalheatconductionequationwithatimefractionalderivativeinthegeneralorthogonalcurvilinearcoordinatesystemisbuilt.Thefractionalheatconductionequationsinotherorthogonalcoordinatesystemsarereadilyobtainableasspecialcases.Inaddition,weobtainthesolutionofthefractionalheatconductionequationinthecylindricalcoordinatesystemintermsofthegeneralizedH-functionusingintegraltransformationmethods.Thefractionalheatconductionequationinthecase0<α≤1interpolatesthestandardheatconductionequation(α=1)andtheLocalizedheatconductionequation(α→0).Finally,numericalresultsarepresentedgraphicallyforvariousvaluesoforderoffractionalderivative.
ThefractionaldiffusionmodelwithanabsorptiontermandmodifiedFick'slawfornon-localtransportprocesses.
Ageneralizednon-localFick’slawonfractal-dimensionisderived.UsingmodifiedFick’slawatime–spacefractionaldiffusionmodelwithafractionaloscillatortermisbuilt.ThesolutionisobtainedintermsofMittag–LefflerfunctionusingfiniteHankelintegraltransformationandLaplacetransformation.Inaddition,numericalsimulationsarediscussed.Theresultsshowthattheeffectrangeoftime-fractionalderivativeνonprobabilitydensityisgreaterthanthatoffractionaloscillatorparameterβ.Theeffectrangeofνonprobabilitydensityisoppositetothatofβ.Thispaperprovidesanewanalyticaltooltodevelopfluidmechanics,heatconductionandotherengineeringscience.
AxialCouetteflowoftwokindsoffractionalviscoelasticfluidsinanannulus.
ThispaperdealswiththeunsteadyaxialCouetteflowoffractionalsecondgradefluid(FSGF)andfractionalMaxwellfluid(FMF)betweentwoinfinitelylongconcentriccircularcylinders.Withthehelpofintegraltransforms(LaplacetransformandWebertransform),generalizedMittag–LefflerfunctionandH-Foxfunction,wegettheanalyticalsolutionsofthemodels.Thenwediscusstheexactsolutionsandfindsomeresultswhichhavebeenknownasspecialcasesofoursolutions.Finally,weanalyzetheeffectsofthefractionalderivativeonthemodelsbyusingthenumericalresultsandfindthattheoscillationexistsinthevelocityfieldofFMF.
SomeexactsolutionstoStefanproblemswithfractionaldifferentialequations.
Someexactsolutionstothefirst,secondandextendedStefanproblemswithfractionaltimederivativedescribedintheCaputosensearegivenbymeansoffractionalGreen'sfunctionandWrightfunctioninthispaper.Bytheaidofsimplecalculations,manyresultsofdifferentialequationsofintegerordercanbeobtainedasspecialcasesoftheresultsgivenbythispaper.
ComparisontheoremsforforwardbackwardSDEs.
WeprovesomecomparisontheoremsforforwardbackwardSDEsin1-dimensionormulti-dimensionbyprobabilisticmethodanddualitytechnique.
Backwardstochasticdifferentialequationswithreflectionandweakassumptionsonthecoefficients.
Inthispaper,westudyreflectedBSDE’swithonecontinuousbarrier,undermonotonicityandgeneralincreasingconditionsinyandnon-Lipschitzconditionsinz.Weprovetheexistenceanduniquenessofasolutionbyanapproximationmethod.
ConvergenceofsolutionsofdiscretereflectedbackwardSDE'sandsimulations.
Theobjectiveofthispaperistointroduceelementarydiscretereflectedbackwardequationsandtogiveasimplemethodtodiscretizeintimea(continuous)reflectedbackwardequation.Apresentationofnumericalsimulationsisalsodescribed.
ReflectedBSDEswithtwobarriersundermonotonicityandgeneralincreasinggrowthconditions.
Inthispaper,weprovetheexistenceanduniquenessresultofthereflectedBSDEwithtwocontinuousbarriersundermonotonicityandgeneralincreasingconditionony,withLipschitzconditiononz.
g-GammaExpectationsandtheRelatedNonlinearDoob-MeyerDecompositionTheorem.
Inthispaper,wedefineanonlinearexpectationviatheBSDEwithconstraint(BSDEwithsigularcoefficient),thenweintroducedefinitionsofsuperandsubmartingaleunderthisnonlinearexpectationandprovetheirnonlinearDoob-Meyertypedecomposition.
ReflectedBackwardStochasticDifferentialEquationswithtwoRCLLbarriers.
InthispaperweconsiderBSDEswithLipschitzcoefficientreflectedontwodiscontinuous(RCLL)barriers.Inthiscase,weprovefirsttheexistenceanduniquenessofthesolution,thenwealsoprovetheconvergenceofthesolutionsofthepenalizedequationstothesolutionoftheRBSDE.Sincethemethodusedinthecaseofcontinuousbarriers(seeCvitanicandKaratzas,Ann.Probab.24(1996)2024–2056andLepeltierandSanMartín,J.Appl.Probab.41(2004)162–175)doesnotwork,wedevelopanewmethod,byconsideringthesolutionsofthepenalizedequationsasthesolutionsofspecialRBSDEsandusingsomeresultsofPengandXuinAnnalesofI.H.P.41(2005)605–630.
ReflectedBSDEsundermonotonicityandgeneralincreasinggrowthconditions.
Weprovetheexistenceanduniquenessofthesolutiontocertainreflectedbackwardstochasticdifferentialequations(RBSDEs)withonecontinuousbarrieranddeterministicterminaltime,undermonotonicity,andgeneralincreasinggrowthconditionsontheassociatedcoefficient.Asanapplication,weobtain,insomeconstraintcases,thepriceofanAmericancontingentclaimastheuniquesolutionofsuchanRBSDE.
Thesmallestg-supermartingaleandreflectedBSDEwithsingleanddoubleL^2obstacles.
InthispaperweshowhowasolutionofBSDEcanbereflectedbyaveryirregularL^2-obstacle.Weprovethatthisproblemisequivalenttofindthesmallestg-supermartingaleofBSDEthatdominatesthisobstacle.WethenobtaintheexistenceanduniquenessandcontinuousdependencetheoremforthisreflectedBSDE.WealsoconsidertheproblemofexistenceanduniquenessofreflectedBSDEwithdoubleL^2obstacles,byusingapenalizationmethod.Anewmonotoniclimittheoremisdevelopedtoprovetheconvergenceofthepenalizationsequence,andtoprovetheexistencetheorem.WealsoprovethatthisreflectedBSDEwithdoubleobstaclesisequivalenttoaproblemofthesmallestg-supermartingaleandthelargestg-submartingale.
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