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1、AbstractWiththeincreasingopening-upanddevelopmentofinsurancemarket,theinsuranceindustryincreasinglycompetitive.Insurancecompaniesneedtodevelopmorecompetitiveproductsconstantly,andthroughthemethodofthereinsurancetoimprovetheleveloftheinsurancecompany’ssurplusand
2、theabilitytoresistrisks.Andtheresearchofthedividendoptimizationproblemsisastandardtomeasuretheprofitleveloftheinsurancecompany,whichhasgreatsignificanceforthemanagementanddecisionsoftheinsurancecompany.Therefore,thiskindofproblemhasbecomethenewresearchhotspotinto
3、day’sinsurance.Inthispaper,weusedtheclassicalcompoundbinomialmodeltoinvesti-gatetheoptimaldividendreinsurancestrategiesindiscreteriskmodel.Thatistosay,westudythedecisionsoftheinsurancecompaniesaftertheinsurancecompanieschargeapremiumandtomakeaclaim,whichenablet
4、heinsurerstomoreefficientworkingcapitalandbettercontrolrisk.Thedecisionisaclassofexpenditurefunctionwithconstantboundarywhichtakeanintegervalueanddependonthecurrentinstantaneoussurplus.inthepaper,theexpenditurefunc-tioncontainsthereinsurancepremiumthatthereinsura
5、ncemaybepurchasedanddividendsthatpaidtoshareholders.Thegoalofthedecisionistomaximizethedividendsofvaluefunction.Wetakeintoaccountpurchasetheexcessoflossreinsuranceandresettingcapitalreinsurancearoundingtheexpenditurefunction,eventuallywefoundthatthevaluefunctio
6、nistheuniquesolutionofadiscreteHamilton-Jacobi-Bellmanequation,andresultingintheoptimalexpenditurepol-icy,dividendpolicyandthecorrespondingoptimalreinsurance.Inthefirstpartofthepaper,weconsidertheexcessoflossreinsuranceandcangettheproblemofthedoublecontrolobject
7、optimization.weusedthemethodofsubstepoptimizationtoconsidertheoverallpayingout(thesituationofnotpurchaseinsurance,onlyconsidersinglecontrolobject)andgetoptimalexpenditures(dividend)policies.atfirst;andthenweusedatransformationofvaluefunctiontogettheasimplecalcul
8、ationmethodoftheoptimalvalueIIfunctionandoptimaldividendpolicy.Afterthis,onthebasisofthefixedoverallexpenditure,consideringperchaseoptimalreinsurancepolicy,wealsogettheoptima
