谱负Levy过程阈值策略的最优性的新证明尹传存心申莹】，YUENKam-Chuen2|曲阜师范大学数学科学学院，曲阜2731652香港大学统计与精算科学系，香港摘要：本文考虑了保险公司的戢优分红问题，其非控制的盈余过程是一个谱负Levy过程。假设分红按照一能的比例分给客户。我们证明了当L6vy测度有一个完全单调的密度时，最优分红策略是阈值策略。关键词：应用概率；谱负Levy过程；最优分红问题；尺度函数；完全单调性；阈值策略中图分类号：0211.6AlternativeapproachtotheoptimalityofthethresholdstrategyforspectrallynegativeLevyprocessesYINChuan-Cum,*,SHENYingi,YUENKam-Chuen21SchoolofMathematicalSciences,QufuNormalUniversity,Qufii2731652DepartmentofStatisticsandActuarialScience,TheUniversityofHongKong,HongKongAbstract:ThispaperconsiderstheoptimaldividendproblemforaninsurancecompanywhoseuncontrolledsurplusprocessevolvesasaspectrallynegativeLevyprocess・Wcassumethatdividendsarcpaidtotheshareholdersaccordingtoadmissiblestrategicswhosedividendrateisboundedbyaconstant.WeshownthatathresholdstrategyformsanoptimalstrategyundertheconditionthattheLevymeasurehasacompletelymonotonedensity.Keywords:Appliedprobability;SpectrallynegativeLevyprocess;Optimaldividendproblem;Scalefunction;Completemonotonicity;Thresholdstrategy0IntroductionTheclassicaloptimaldividendproblemlooksforthestrategythatmaximizestheexpecteddiscounteddividendpaymentsuntilruininaninsuranceportfolio,whichhasrecentlyreceivedalotofattentioninactuarialmathematics.ThisoptimizationproblemwasfirstproposedbyDeFinetti(1957)toreflectmorerealisticallythesurpluscashflowsinaninsuranceportfolio,whoII:TheNationalNaturalScienceFoundationofChina(GrantNo.11171179).theResearchFundfortheDoctoralProgramofHigherEducationofChina(No.20093705110002).作者简介：YINChuan-Cun(1963-)•male,professor,majorresearchdirection：StochasticProcesses.Correspondenceauthor：YINChuan-Cun(1963-),male*professor^majorresearchdirection：StochasticProcesses.consideredadiscretetimerandomwalkwithstepsizes土1andprovedthattheoptimaldividendstrategyisabarrierstrategy.Sincethenmanyresearchershavetriedtoaddressthisoptimalityquestionundermoregeneralandmorerealisticmodelassumptionsanduntilnowadaysthisturnsouttobearichandchallengingfieldofresearchthatneedsthecombinationoftoolsfromanalysis,probabilityandstochasticcontrol.FortheclassicalcompoundPoissonriskmodel,thisproblemwassolvedbyGerberin(1969)viaalimitofanassociateddiscreteproblem.Recently,thisoptimaldividendproblemintheclassicalcompoundPoissonriskmodelandalsoincludedageneralreinsurancestrategyasasecondcontrolpossibilitywastakenupagainbyAzcueandMuler(2005),whousedstochasticcontroltheoryandviscositysolutions・Forallthesecasesingeneralabandstrategyturnsouttobeoptimalamongalladmissiblestrategies.Inparticular,forexponentiallydistributedclaimsizesthisoptimalstrategysimplifiestoabarrierstrategy.InAlbrecherandThonhauser(2008)itisshownthattheoptimalityofbarrierstrategiesintheclassicalmodelwithexponentialclaimsstillholdsifthereisaconstantforceofinterest.Avrametal.(2007)consideredthecasewheretheriskprocessisgivenbyageneralspectrallynegativeLevyprocessandgaveasufficientconditioninvolvingthegeneratoroftheLevyprocessforoptimalityofthebarrierstrategy.Recently,Loeffen(2008)showedthatbannerstrategyisoptimalamongalladmissiblestrategiesforgeneralspectrallynegativeLevyriskprocesseswithcompletelymonotonejumpdensity,andKyprianouctal.(2010)relaxedthisconditiononthejumpdensitytolog-conve...