[16]Darrell Duffie - Dynamic asset pricing theory(Provisional Manuscript)

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1、DynamicAssetPricingTheory(ProvisionalManuscript)DarrellDuffieGraduateSchoolofBusinessStanfordUniversityPreliminaryIncompleteDraft:NotforDistributionCopyrightc1999DarrellDuffieOctober5,1999iiContents1IntroductiontoStatePricing91AArbitrageandStatePrices....................91BRisk-NeutralProbabilit

2、ies....................101COptimalityandAssetPricing..................111DEfficiencyandCompleteMarkets................141EOptimalityandRepresentativeAgents.............151FState-PriceBetaModels.....................182TheBasicMultiperiodModel292AUncertainty............................292BSecuri

3、tyMarkets.........................302CArbitrage,StatePrices,andMartingales............302DIndividualAgentOptimality...................332EEquilibriumandParetoOptimality...............342FEquilibriumAssetPricing....................352GArbitrageandMartingaleMeasures...............362HValuation

4、ofRedundantSecurities................392IAmericanExercisePoliciesandValuation............402JIsEarlyExerciseOptimal?....................443TheDynamicProgrammingApproach613ATheBellmanApproach......................613BFirst-OrderConditionsoftheBellmanEquation........633CMarkovUncertainty......

5、..................633DMarkovAssetPricing.......................643ESecurityPricingbyMarkovControl...............653FArbitrage-FreeValuationinaMarkovSetting.........673GEarlyExerciseandOptimalStopping..............69ivCONTENTS4TheInfinite-HorizonSetting794AMarkovDynamicProgramming.............

6、....794BDynamicProgrammingandEquilibrium............834CArbitrageandStatePrices....................844DOptimalityandStatePrices...................854EMethod-of-MomentsEstimation.................875TheBlack-ScholesModel975ATradingGainsforBrownianPrices...............975BMartingaleTradingGains

7、....................995CItoPricesandGains.......................1005DIto’sFormula...........................1025ETheBlack-ScholesOption-PricingFormula...........1025FBlack-ScholesFormula:FirstTry................1045GThePDEforArbitrage-FreeDerivativ