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带有分红和交易费用的比例再保险最佳控制模型.docx

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带有分红和交易费用的比例再保险最佳控制模型 Title:OptimalControlModelforReinsurancewithDividendsandTransactionCosts Abstract: Reinsuranceplaysacrucialroleinriskmanagementforinsurancecompanies.Inrecentyears,theincorporationofdividendsandtransactioncostsinreinsurancemodelshasgainedattentionduetotheirpotentialimpactondecision-makingprocesses.Thispaperaimstodevelopanoptimalcontrolmodelforreinsurancethatconsidersbothdividendsandtransactioncosts.Themodelaimstomaximizethetotalexpectedutilityoftheinsurer'sterminalwealth,subjecttocertainconstraints. 1.Introduction Reinsuranceisariskmanagementstrategyemployedbyinsurancecompaniestotransferaportionoftheirriskstootherparties.Traditionalreinsurancemodelsfocusondeterminingtheoptimalretentionleveltominimizetheinsurer'sruinprobabilityormaximizetheexpectedutilityofterminalwealth.However,theinclusionofdividendsandtransactioncostscansignificantlyinfluencethedecision-makingprocess. 2.LiteratureReview Previousstudieshaveprimarilyfocusedonreinsurancemodelswithoutconsideringdividendsortransactioncosts.Someliteraturehasexploredtheimpactofdividendsortransactioncostsseparatelyonreinsurancedecisions.However,thereisalackofliteraturethatcombinesbothaspectsintoacomprehensivemodel. 3.ModelDevelopment Inthisstudy,weconsideracontinuous-timedynamicreinsurancecontrolmodelwithstochasticprocesses.Theaimistodeterminetheoptimalcontrolstrategiesthatmaximizethetotalexpectedutilityoftheinsurer'sterminalwealth,whileconsideringdividendsandtransactioncosts.Themodelincorporatesseveralkeycomponents: 3.1.Dividends Dividendsrepresentthedistributionofsurplusprofitstotheinsurer'sshareholders.Inourmodel,dividendpaymentswillimpacttheinsurer'swealthaccumulationandreservelevels.Weutilizeageneraldividendprocesstocapturevariousdividendpaymentstrategies. 3.2.TransactionCosts Transactioncostsaretheexpensesincurredduringtheexecutionofreinsurancecontracts.Thesecostsariseduetobrokeragefees,administrativeexpenses,legalfees,etc.Ourmodelconsiderstransactioncostsasapercentageofthetotalreinsurancepremium