套利数学

图书标准信息

• 作者 [瑞士]戴尔贝恩 著
• 出版社 世界图书出版公司
• 出版时间 2010-09
• 版次 1
• ISBN 9787510027376
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 373页
• 正文语种 英语

【内容简介】

in1973f.blackandm.scholespublishedtheirpathbreakingpaper[bs73]onoptionpricing.thekeyidea--attributedtor.meltoninafootnoteoftheblack-scholespaper--istheuseoftradingincontinuoustimeandthenotionofarbitrage.thesimpleandeconomicallyveryconvincingprincipleofno-arbitrage"allowsonetoderive，incertainmathematicalmodelsoffinancialmarkets（suchasthesamuelsonmodel，[s65]，nowadaysalsoreferredtoasthe"black-scholes"model，basedongeometricbrownianmotion），uniquepricesforoptionsandothercontingentclaims.
thisremarkableachievementbyf.black，m.scholesandr.mertonhadaprofoundeffectonfinancialmarketsanditshiftedtheparadigmofdeal-ingwithfinancialriskstowardstheuseofquitesophisticatedmathematicalmodels.

【目录】

PartIAGuidedTourtoArbitrageTheory
1TheStoryinaNutshell
1.1Arbitrage
1.2AnEasyModelofaFinancialMarket
1.3PricingbyNo-Arbitrage
1.4VariationsoftheExample
1.5MartingaleMeasures
1.6TheFundamentalTheoremofAssetPricing
2ModelsofFinancialMarketsonFiniteProbabilitySpaces
2.1DescriptionoftheModel
2.2No-ArbitrageandtheFundamentalTheoremofAssetPricing
2.3EquivalenceofSingle-periodwithMultiperiodArbitrage
2.4PricingbyNo-Arbitrage
2.5ChangeofNumeraire
2.6KramkovsOptionalDecompositionTheorem
3UtilityMaximisationonFiniteProbabilitySpaces
3.1TheCompleteCase
3.2TheIncompleteCase
3.3TheBinomialandtheTrinomialModel
4BachelierandBlack-Scholes
4.1IntroductiontoContinuousTimeModels
4.2ModelsinContinuousTime
4.3BacheliersModel
4.4TheBlack-ScholesModel
5TheKreps-YanTheorem
5.1AGeneralFramework
5.2NoFreeLunch
6TheDalang-Morton-WillingerTheorem
6.1StatementoftheTheorem
6.2ThePredictableRange
6.3TheSelectionPrinciple
6.4TheClosednessoftheConeC
6.5ProofoftheDalang-Morton-WillingerTheoremforT=1
6.6AUtility-basedProofoftheDMWTheoremforT=1
6.7ProofoftheDalang-Morton-WillingerTheoremforT≥1byInductiononT
6.8ProofoftheClosednessofKintheCaseT≥1
6.9ProofoftheClosednessofCintheCaseT≥1underthe（NA）Condition
6.10ProofoftheDalang-Morton-WillingerTheoremforT≥1usingtheClosednessofC
6.11InterpretationoftheL-BoundintheDMWTheorem...
7APrimerinStochasticIntegration
7.1TheSet-up
7.2IntroductoryonStochasticProcesses
7.3Strategies，Semi-martingalesandStochasticIntegration
8ArbitrageTheoryinContinuousTime：anOverview
8.1NotationandPreliminaries
8.2TheCrucialLemma
8.3Sigma-martingalesandtheNon-locallyBoundedCase

PartIITheOriginalPapers
9AGeneralVersionoftheFundamentalTheoremofAssetPricing（1994）
9.1Introduction
9.2DefinitionsandPreliminaryResults
9.3NoFreeLunchwithVanishingRisk
9.4ProofoftheMainTheorem
9.5TheSetofRepresentingMeasures
9.6NoFreeLunchwithBoundedRisk
9.7SimpleIntegrands
9.8Appendix：SomeMeasureTheoreticalLemmas
10ASimpleCounter-ExampletoSeveralProblemsintheTheoryofAssetPricing（1998）
10.1IntroductionandK~iownResults.
10.2ConstructionoftheExample
10.3IncompleteMarkets
11TheNo-ArbitragePropertyunderaChangeofNumeraire（1995）
11.1Introduction
11.2BasicTheorems
11.3DualityRelation
11.4HedgingandChangeofNumraire
12TheExistenceofAbsolutelyContinuousLocalMartingaleMeasures（1995）
12.1Introduction
12.2ThePredictableRadon-NikodymDerivative
12.3TheNo-ArbitragePropertyandImmediateArbitrage.，
12.4TheExistenceofanAbsolutelyContinuous
LocalMartingaleMeasure
13TheBanachSpaceofWorkableContingentClaimsinArbitrageTheory（1997）
13.1Introduction
13.2MaximalAdmissibleContingentClaims
13.3TheBanachSpaceGeneratedbyMaximalContingentClaims
13.4SomeResultsontheTopologyof
13.5TheValueofMaximalAdmissibleContingentClaimsontheSetMe
13.6TheSpacesunderaNumdraireChange
13.7TheClosureofsandRelatedProblems
14TheFundamentalTheoremofAssetPricingforUnboundedStochasticProcesses（1998）
14.1Introduction
14.2Sigma-martingales
14.3One-periodProcesses
14.4TheGeneralRd-valuedCase
14.5DualityResultsandMaximalElements
15ACompactnessPrincipleforBoundedSequencesofMartingaleswithApplications（1999）
15.1Introduction
15.2NotationsandPreliminaries
15.3AnExample
15.4ASubstituteofCompactnessforBoundedSubsetsofH1
15.4.1ProofofTheorem15.A
15.4.2ProofofTheorem15.C
15.4.3ProofofTheorem15.B
15.4.4AproofofM.YorsTheorem..
15.4.5ProofofTheorem15.D
15.5Application
PartIIIBibliography
References