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1、Regression-basedMonteCarlomethodsforstochasticcontrolmodels:VariableannuitieswithlifelongguaranteesYaoTungHuangandYueKuenKwokDepartmentofMathematicsHongKongUniversityofScienceandTechnologyHongKong,ChinaAbstractWepresenttheregression-basedMonteCarlosimulationalg
2、orithmsforsolvingthestochasticcontrolmodelsassociatedwithpricingandhedgingoftheGuaranteedLifelongWithdrawalBenefit(GLWB)invariableannuities,wherethedynamicsoftheunderlyingfundvalueisassumedtoevolveaccordingtothestochasticvolatilitymodel.TheGLWBoffersalifelongwithd
3、rawalbenefitevenwhenthepolicyaccountvaluebecomeszerowhilethepolicyholderremainsalive.Upondeath,theremainingaccountvaluewillbepaidtotheben-eficiaryasadeathbenefit.Thebang-bangcontrolstrategyanalyzedundertheassumptionofmaximizationofthepolicyholder’sexpectedcashflowre
4、ducesthestrategyspaceofoptimalwithdrawalpoliciestothreechoices:zerowithdrawal,withdrawalatthecontractualamountorcompletesurrender.TheimpactontheGLWBvalueundervariouswithdrawalbehaviorsofthepolicyholderisexamined.WealsoanalyzethepricingpropertiesofGLWBsubjecttodi
5、fferentmodelparametervaluesandstructuralfeatures.JELclassification:G22,C50Keywords:variableannuities,lifelongwithdrawalguarantees,stochasticcontrolmodels,MonteCarlosimu-lation,regression-basedalgorithms,stochasticvolatility1IntroductionThemarketforvariableannuitie
6、shasshownphenomenalgrowthsince1990s.Attheendof2011,thetotalassetsofvariableannuitiestoppedUSD1.5trillion.Assweetenerstoattractbusinesses,issuersofvariableannuitiesprovidevariousformsofguaranteesriderstoinvestors,besidesequityparticipationwithinvestmentchoicesamo
7、ngalistofmutualfunds.Theseguaranteescanbeclassifiedintotwobroadtypes:guaranteedminimumdeathbenefits(GMDBs)andguaranteedminimumlivingbenefits(GMLBs).Thesecondtypecanbefurtherclassifiedintothreesubtypes,namely,guaranteedminimumaccumulationbenefits(GMABs),guaranteedmini
8、mumincomebenefits(GMIBs)andguaranteedminimumwithdrawalbenefits(GMWBs).AgoodcomprehensivesummaryofthestructuralfeaturesofthesebenefitscanbefoundinBaueretal.(2008)andBacin
