Optimal investment and excess-of-lossre insurance problem with delay for an insurer under Heston's SV model

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1、Insurance:MathematicsandEconomics61(2015)181–196ContentslistsavailableatScienceDirectInsurance:MathematicsandEconomicsjournalhomepage:www.elsevier.com/locate/imeOptimalinvestmentandexcess-of-lossreinsuranceproblemwithdelayforaninsurerunderHeston’sSVmodelChunxiangAa,b,ZhongfeiLic,∗aSch

2、oolofMathematicsandComputationalScience,SunYat-senUniversity,Guangzhou510275,PRChinabSchoolofMathematicsandStatistics,ZhaoqingUniversity,Guangdong,526061,PRChinacSunYat-senBusinessSchool,SunYat-senUniversity,Guangzhou510275,PRChinahighlights•Theoptimalinvestmentandexcess-of-lossreinsu

3、ranceproblemwithdelayisconsidered.•TheriskyassetismodeledastheHeston’sSVmodels.•Thedynamicprogrammingapproachwithdelayisapplied.•Theinsurer’saimistomaximizingexpectedexponentialutilityfromterminalwealth.articleinfoabstractArticlehistory:Thispaperconsidersanoptimalinvestmentandexcess-o

4、f-lossreinsuranceproblemwithdelayforanReceivedMay2014insurerunderHeston’sstochasticvolatility(SV)model.SupposethattheinsurerisallowedtopurchaseReceivedinrevisedformexcess-of-lossreinsuranceandinvestshersurplusinafinancialmarketconsistingofonerisk-freeassetDecember2014andoneriskyassetw

5、hosepriceprocessisdescribedbyHeston’sSVmodel.UndertheconsiderationoftheAccepted13January2015performance-relatedcapitalinflow/outflow,thewealthprocessoftheinsurerismodeledbyastochasticAvailableonline21January2015differentialdelayequation.Theinsurer’saimistomaximizetheexpectedexponentia

6、lutilityofthecombinationofterminalwealthandaverageperformancewealth.ByadoptingthedynamicprogrammingMSC:approach,theoptimalstrategiesandtheoptimalvaluefunctionsarederivedexplicitlyundertwocases:IM52IE13theinvestment-reinsurancecaseandtheinvestment-onlycase.Finally,somenumericalexamples

7、andIB91sensitivityanalysisareprovidedforourresults.©2015ElsevierB.V.Allrightsreserved.Keywords:Excess-of-lossreinsuranceHeston’sstochasticvolatilitymodelStochasticdifferentialdelayequationHamilton–Jacobi–BellmanequationInsurer1.Introductiontheirriskexposurestotheseriskyassets.Moreover

8、,inco