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1、Chapter15MONTECARLOSIMULATIONANDNUMERICALINTEGRATIONJOHNGEWEKE*UniversityofMinnesotaandFederalReserveBankofMinneapolisContents1.Introduction7332.Deterministicmethodsofintegration7342.1.Unidimensionalquadrature7342.2.Multidimensionalquadrature7352.3.Lowdiscrepancymet
2、hods7382.4.Otherdeterministicmethods7413.Pseudorandomnumbergeneration7423.1.Uniformpseudorandomnumbergeneration7433.2.Generalmethodsfornonuniformdistributions7453.3.Selectedunivariatedistributions7523.4.Selectedmultivariatedistributions7544.IndependenceMonteCarlo756
3、4.1.SimpleMonteCarlo7574.2.Acceptancemethods7594.3.Importancesampling7614.4.Anoteonthechoiceofmethod7645.Variancereduction7695.1.AntitheticMonteCarlo7705.2.Systematicsampling7725.3.Theuseofconditionalexpectations7735.4.Controlvariables774*CommentsfromJohnRustandtwoa
4、nonymousreferees,whobearnoresponsibilityforerrorsoromissions,aregratefullyacknowledged.ThisworkwassupportedinpartbyNationalScienceFoundationGrantsSES-9210070andSBR-9514865.TheviewsexpressedinthispaperarethoseoftheauthorandnotnecessarilythoseoftheFederalReserveBankof
5、MinneapolisortheFederalReserveSystem.HandbookofComputationalEconomics,VolumeLEditedbyH.M.Amman,D.A.KendrickandJ.Rust@1996ElsevierScienceB.EAllrightsreserved.7321.Geweke6.MarkovchainMonteCarlomethods7756.1.TwoMarkovchainMonteCarloalgorithms7776.2.Mathematicalbackgrou
6、nd7796.3.ConvergenceoftheGibbssampler7816.4.ConvergenceoftheMetropolis-Hastingsalgorithm7846.5.Assessingconvergenceandnumericalaccuracy7857.Someexamples7887.1.Stochasticvolatility7887.2.Integrationandoptimization793References797Ch.15:MonteCarloSimulationandNumerical
7、Integration7331.IntroductionOptimizationproblemsindynamic,stochasticenvironmentsareanincreasinglyim-portantpartofeconomictheoryandappliedeconomics.Inspiredbythepotentialreturnstoricherandmorerealisticmodelsofavarietyofpolicyproblemsandthepromiseofever-growingcomputa
8、tionalpower,economistshaveturnedmoreandmoretomodelsthatcanbesimulatedbutnotsolvedinclosedform.Simulationmethodscanprovidesolutionsfortwore
