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1、StatisticsandProbabilityLetters106(2015)134–141ContentslistsavailableatScienceDirectStatisticsandProbabilityLettersjournalhomepage:www.elsevier.com/locate/staproOptimalreinsurancewithbothproportionalandfixedcostsPengLia,MingZhoub,∗,ChuancunYincaSchoolo
2、fInsurance,CentralUniversityofFinanceandEconomics,Beijing100081,ChinabChinaInstituteforActuarialScience,CentralUniversityofFinanceandEconomics,Beijing100081,ChinacSchoolofMathematicalSciences,QufuNormalUniversity,Shandong273165,Chinaarticleinfoabstract
3、Articlehistory:ThispaperinvestigatesanoptimalreinsuranceproblemwithbothproportionalandfixedReceived5February2015transactioncosts.Associatedwithareinsurance,theproportionalcostisusuallychargedbyReceivedinrevisedform9June2015thereinsurerandthefixedcostoc
4、cursatthebeginningofthereinsuranceduetoconsultantAccepted20June2015commission.Wedescribeaninsurer’soriginalcashreserveprocessbyaBrownianmotionAvailableonline7July2015withpositivedrift.Theinsureraimstominimizeitsruinprobabilitybytakingadynamicreinsuranc
5、estrategy.Thisleadstoamixedregularcontrolandoptimalstoppingproblem.Keywords:Wesolveitbyestablishingaconnectionwithanoptimalstoppingproblem.ThevalueIrreversiblereinsurancefunctionandtheoptimalreinsurancestrategyareobtainedexplicitly.Mixedregularcontrol/
6、optimalstoppingproblem©2015ElsevierB.V.Allrightsreserved.FixedcostProportionalcost1.IntroductionInpractice,reinsuranceisanimportantwayforaninsurertocontrolitsriskexposure.Therefore,inthepastfewdecades,theoptimalreinsuranceproblemhasbeenextensivelystudi
7、edforvariousobjectivefunctionsinmathematicalfinanceliterature.Thepopularobjectivefunctionsinclude,butnotlimitto,minimizingruinprobabilityandmaximizingpresentvalueofdividendpayments.Tonameafew,Browne(1995),Schmidli(2001),Zhangetal.(2007)andPromislowandY
8、oung(2005)studiedtheoptimal(proportional,excess-of-loss,orother)reinsurancebyminimizingtheruinprobability;Taksar(2000)andHøjgaardandTaksar(2004)consideredtheoptimalreinsuranceproblembymaximizingthefirmvalue,thatistheexpectedpresentvalue
