Optimal Control Theory with Applications in Economics

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1、OptimalControlTheorywithApplicationsinEconomicsOptimalControlTheorywithApplicationsinEconomicsThomasA.WeberForewordbyA.V.KryazhimskiyTheMITPressCambridge,MassachusettsLondon,England©2011MassachusettsInstituteofTechnologyAllrightsreserved.Nopartofthisbookmayberepr

2、oducedinanyformbyanyelec-tronicormechanicalmeans(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthepublisher.Forinformationaboutspecialquantitydiscounts,pleaseemailspecial_sales@mitpress.mit.edu.ThisbookwassetinPala

3、tinobyWestchesterBookComposition.PrintedandboundintheUnitedStatesofAmerica.LibraryofCongressCataloging-in-PublicationDataWeber,ThomasA.,1969–Optimalcontroltheorywithapplicationsineconomics/ThomasA.Weber;forewordbyA.V.Kryazhimskiy.p.cm.Includesbibliographicalrefer

4、encesandindex.ISBN978-0-262-01573-8(hardcover:alk.paper)1.Economics—Mathematicalmodels.2.Controltheory.3.Mathematicaloptimization.4.Gametheory.I.Title.HB135.W4332011330.01515642—dc22201004648210987654321ForWimContentsForewordbyA.V.KryazhimskiyixAcknowledgmentsxi

5、1Introduction11.1Outline31.2Prerequisites51.3ABriefHistoryofOptimalControl51.4Notes152OrdinaryDifferentialEquations172.1Overview172.2First-OrderODEs202.3Higher-OrderODEsandSolutionTechniques672.4Notes752.5Exercises763OptimalControlTheory813.1Overview813.2ControlS

6、ystems833.3OptimalControl—AMotivatingExample883.4Finite-HorizonOptimalControl1033.5Infinite-HorizonOptimalControl1133.6Supplement1:AProofofthePontryaginMaximumPrinciple1193.7Supplement2:TheFilippovExistenceTheorem1353.8Notes1403.9Exercises141viiiContents4GameTheor

7、y1494.1Overview1494.2FundamentalConcepts1554.3DifferentialGames1884.4Notes2024.5Exercises2035MechanismDesign2075.1Motivation2075.2AModelwithTwoTypes2085.3TheScreeningProblem2155.4NonlinearPricing2205.5Notes2265.6Exercises227AppendixA:MathematicalReview231A.1Algeb

8、ra231A.2NormedVectorSpaces233A.3Analysis240A.4Optimization246A.5Notes251AppendixB:SolutionstoExercises253B.1NumericalMethods253B.2OrdinaryDifferentialEquations