连续时间中的随机优化

图书标准信息

• 作者 [美]Fwu-Ranq Chang 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 1
• ISBN 9787510050442
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 326页

【内容简介】

　　"Stochasticoptimizationincontinuoustime"（AuthorFwu-RanqChang）isarigorousbutuser-friendlybookontheapplicationofstochasticcontroltheorytoeconomics.Adistinctivefeatureofthebookisthatmath-ematicalconceptsareintroducedinalanguageandterminologyfamiliartograduatestudentsofeconomics.

【目录】

ListofFigures
Preface
1ProbabilityTheory
1.1Introduction
1.2StochasticProcesses
1.2.1InformationSetsanda-Algebras
1.2.2TheCantorSet
1.2.3Borel-CantelliLemmas
1.2.4DistributionFunctionsandStochasticProcesses
1.3ConditionalExpectation
1.3.1ConditionalProbability
1.3.2ConditionalExpectation
1.3,3ChangeofVariables
1.4NotesandFurtherReadings
2WienerProcesses
2.1introduction
2.2AHeuristicApproach
2.2.1FromRandomWalkstoWienerProcess
2.2.2SomeBasicPropertiesoftheWienerProcess
2.3MarkovProcesses
2.3.1Introduction
2.3.2TransitionProbability
2.3.3DiffusionProcesses
2.4WienerProcesses
2.4.1HowtoGenerateMoreWienerProcesses
2.4.2DifferentiabilityofSampleFunctions
2.4.3StoppingTimes
2.4.4TheZeroSet
2.4.5BoundedVariationsandtheIrregularityofthe
WienerProcess
2.5NotesandFurtherReadings
3StochasticCalculus
3.1Introduction
3.2AHeuristicApproach
3.2.1ls□（sX）dWsRiemarmIntegrable?
3.2.2TheChoiceof□Matters
3.2.3InSearchoftheClassofFunctionsfora（s,w）
3.3TheItoIntegral
3.3.1Definition
3.3.2Martingales
3.4lto'sLemma:AutonomousCase
3.4.1Ito'sLemma
3.4.2GeometricBrownianMotion
3.4.3PopulationDynamics
3.4.4AdditiveShocksorMultiplicativeShocks
3.4.5MultipleSourcesofUncertainty
3.4.6Multivariatelto'sLemma
3.5Ito'sLemmaforTime-DependentFunctions
3.5.1Euler'sHomogeneousDifferentialEquationandtheHeatEquation
3.5.2Black-ScholesFormula
3.5.3IrreversibleInvestment
3.5.4BudgetEquationforanInvestor
3.5.5Ito'sLemma:GeneralForm
3.6NotesandFurtherReadings
4StochasticDynamicProgramming
4.1Introduction
4.2BellmanEquation
4.2.1Infinite-HorizonProblems
4.2.2VerificationTheorem
4.2.3Finite-HorizonProblems
4.2.4ExistenceandDifferentiabilityoftheValueFunction
4.3EconomicApplications
4.3.1ConsumptionandPortfolioRules
4.3.2IndexBonds
4.3.3ExhaustibleResources
4.3.4AdjustmentCostsand（Reversible）Investment
4.3.5UncertainLifetimesandLifeInsurance
4.4Extension:ReeursiveUtility
4.4.1BellmanEquationwithRecursiveUtility
4.4.2EffectsofReeursivity:DeterministicCase
4.5NotesandFurtherReadings
5HowtoSolveit
5.1Introduction
5.2HARAFunctions
5.2.1TheMeaningofEachParameter
5.2.2Closed-FormRepresentations
5.3TrialandError
5.3.1Linear-QuadraticModels
5.3.2Linear-HARAmodels
5.3.3Linear-ConcaveModels
5.3,4Nonlinear-ConcaveModels
5.4Symmetry
5.4.1Linear-QuadraticModelRevisited
5.4.2Merton'sModelRevisited
5.4.3Fischer'sIndexBondModel
5.4.4LifeInsurance
5.5TheSubstitutionMethod
5.6MartingaleRepresentationMethod
5.6.1GirsanovTransformation
5.6.2Example:APortfolioProblem
5.6.3Which8toChoose?
5.6.4ATransformedProblem
5.7InverseOptimumMethod
5.7.1TheInverseOptimalProblem:CertaintyCase
5.7.2TheInverseOptimalProblem:StochasticCase
5.7.3InverseOptimalProblemofMerton'sModel
5.8NotesandFurtherReadings
6BoundariesandAbsorbingBarriers
6.1Introduction
6.2NonnegativityConstraint
6.2.1IssuesandProblems
6.2.2ComparisonTheorems
6.2.3ChangandMalliaris'sReflectionMethod
6.2.4InaccessibleBoundaries
6.3OtherConstraints
6.3.1APortfolioProblemwithBorrowingCoosWaints
6.3.2ViscositySolutions
6.4StoppingRules-CertaintyCase
6.4.1TheBaumol-TobinModel
6.4.2ADynamicModelofMoneyDemand
6.4.3TheTree-CuttingProblem
6.5TheExpectedDiscountFactor
6.5.1FundamentalEquationforEx[e□]
6.5.2OneAbsorbingBarrier
6.5.3TwoAbsorbingBarriers
6.6OptimalStoppingTimes
6.6.1DynamicandStochasticDemandforMoney
6.6.2StochasticTree-CuttingandRotationProblems
6.6.3InvestmentTiming
6.7NotesandFurtherReadings
AMiscellaneousApplicationsandExercises
Bibliography
Index