內容簡介
增加的內容有：一致性風險測度及其在對沖中的套用；一般離散市場模型中資產估價的第一基本定理；不完全離散市場的套利區間；完全離散市場的特徵；Black-Scholes模型中的風險、回報和靈敏度。本書內容安排相當謹慎、詳細，而不是泛泛羅列所有儘可能多的內容，對期權的處理相當精闢。通過本書的學習，讀者也可以了解更多的科研動態。目次：套利定價；鞅測度；第一基本定理；完全市場；離散時間美國期權；連續時間隨機計算；美國賣方期權；債券和期限結構；消費投資策略；風險度量。讀者對象：數學專業的研究生、科研人員以及具有一定數學背景的金融愛好者。
目錄
PrefacePrefacetotheSecondEdition
1PrlcingbyArbitrage
1.1Introduction：PricingandHedging
1.2Single-PeriodOptionPricingModels
1.3AGeneralSingle-PeriodModel
1.4ASingle-PeriodbinomialModel
1.5Multi-periodBinomialModels
1.6BoundsonOptionPrices
2martingaleMeasures
2.1AGeneralDiscrete-TimeMarketModel
2.2tradingStrategies
2.3MartingalesandRisk-NeutralPricing
2.4ArbitragePricing：MartingaleMeasures
2.5StrategiesUsingcontingentClaims
2.6Example：TheBinomialModel
2.7FromCRRtoBlaek-Scholes
3TheFirstFundamentalTheorem
3.1TheSeparatingHyperplaneTheoreminRn
3.2ConstructionofMartingaleMeasures
3.3PathwiseDescription
3.4Examples
3.5GeneralDiscreteModels
4CompleteMarkets
4.1CompletenessandMartingaleRepresentation
4.2CompletenessforFiniteMarketModels
4.3TheCRRModel
4.4TheSplittingIndexandCompleteness
4.5IncompleteModels：TheArbitrageInterval
4.6CharacterisationofCompleteModels
5Discrete-timeAmericanOptions
5.1HedgingAmericanClaims
5.2StoppingTimesandStoppedProcesses
5.3uniformlyIntegrableMartingales
5.4OptimalStopping：TheSnellEnvelope
5.5PricingandHedgingAmericanOptions
5.6Consumption-InvestmentStrategies
6Continuous-TimeStochasticCalculus
6.1Continuous-TimeProcesses
6.2Martingales
6.3StochasticIntegrals
6.4TheIt8Calculus
6.5StochasticDifferentialEquations
6.6MarkovPropertyofSolutionsofSDEs
7Continuous-TimeEuropeanOptions
7.1Dynamics
7.2GirsanovsTheorem
7.3MartingaleRepresentation
7.4Self-FinancingStrategies
7.5AnEquivalentMartingaleMeasure
7.6Black-ScholesPrices
7.7PricinginaMultifactorModel
7.8BarrierOptions
7.9TheBlack-ScholesEquation
7.10TheGREEKS
8TheAmericanPutOption
8.1ExtendedTradingStrategies
8.2AnalysisofAmericanPutOptions
8.3ThePerpetualPutOption
8.4EarlyExercisePremium
8.5RelationtoFreeBoundaryProblems
8.6AnApproximateSolution
9BondsandTermStructure
9.1MarketDynamics
9.2FuturePriceandFuturesContracts
9.3ChangingNumeraire
9.4AGeneralOptionPricingFormula
9.5TermStructureModels
9.6Short-rateDiffusionModels
9.7TheHeath-Jarrow-MortonModel
9.8AMarkovChainModel
10Consumption-InvestmentStrategies
10.1UtilityFunctions
10.2admissibleStrategies
10.3MaximisingUtilityofConsumption
10.4MaximisationofTerminalUtility
10.5ConsumptionandTerminalWealth
11MeasuresofRisk
11.1ValueatRisk
11.2CoherentRiskMeasures
11.3DeviationMeasures
11.4HedgingStrategieswithshortfallRisk
Bibliography
Index
前言
Thisworkisaimedatanaudiencewithasoundmathematicalbackgroundwishingtolearnabouttherapidlyexpandingfieldofmathematicalfinance.Itscontentissuitableparticularlyforgraduatestudentsinmathematicswhohaveabackgroundinmeasuretheoryandprobability.Theemphasisthroughoutisondevelopingthemathematicalconceptsrequiredforthetheorywithinthecontextoftheirapplication.Noattemptismadetocoverthebewilderingvarietyofnovel（orexotic）financialin-strumentsthatnowappearonthederivativesmarkets;thefocusthrough-outremainsonarigorousdevelopmentofthemorebasicoptionsthatlieattheheartoftheremarkablerangeofcurrentapplicationsofmartingaletheorytofinancialmarkets.
Thefirstfivechapterspresentthetheoryinadiscrete-timeframework.Stochasticcalculusisnotrequired，andthismaterialshouldbeaccessibletoanyonefamiliarwithelementaryprobabilitytheoryandlinearalgebra.
Thebasicideaofpricingbyarbitrage（or，rather，bynon-arbitrage）ispresentedinChapter1.TheuniquepriceforaEuropeanoptioninasingle-periodbinomialmodelisgivenandthenextendedtomulti-periodbinomialmodels.Chapter2introducestheideaofamartingalemeasureforpriceprocesses.Followingadiscussionoftheuseofself-financingtrad-ingstrategiestohedgeagainsttradingrisk，itisshownhowoptionscanbepricedusinganequivalentmeasureforwhichthediscountedpricepro-cessisamartingale.ThisisillustratedforthesimplebinomialCox-Ross-Rubinsteinpricingmodels，andtheBlack-Scholesformulaisderivedasthelimitofthepricesobtainedforsuchmodels.Chapter3givesthefunda-mentaltheoremofassetpricing，whichstatesthatifthemarketdoesnotcontainarbitrageopportunitiesthereisanequivalentmartingalemeasure.Explicitconstructionsofsuchmeasuresaregiveninthesettingoffinitemarketmodels.CompletenessofmarketsisinvestigatedinChapter4;inacompletemarket，everycontingentclaimcanbegeneratedbyanadmissibleself-financingstrategy（andthemartingalemeasureisunique）.Stoppingtimes，martingaleconvergenceresults，andAmericanoptionsarediscussedinadiscrete-timeframeworkinChapter5.
精彩書摘
Theunreasonableeffectivenessofmathematicsisevidencedbythefre-quencywithwhichmathematicaltechniquesthatweredevelopedwithoutthoughtforpracticalapplicationsfindunexpectednewdomainsofappli-cabilityinvariousspheresoflife.Thisphenomenonhascustomarilybeenobservedinthephysicalsciences;inthesocialsciencesitsimpacthasper-HAPSbeenlessevident.Oneofthemoreremarkableexamplesofsimulta-neousrevolutionsineconomictheoryandmarketpracticeisprovidedbytheopeningoftheworldsfirstoptionsexchangeinChicagoin1973,andtheground-breakingtheoreticalpapersonpreference-freeoptionpricingbyBlackandScholes[27]（quicklyextendedbyMerton[222]）thatappearedinthesameyear,thusprovidingaworkablemodelfortherationalmarketpricingoftradedoptions.Fromthesebeginnings,financialderivativesmarketsworldwidehavebecomeoneofthemostremarkablegrowthindustriesandnowconstituteamajorsourceofemploymentforgraduateswithhighlevelsofmathemat-icalexpertise.Theprincipalreasonforthisphenomenonhasitsoriginsinthesimultaneousstimulijustdescribed,andtheexplosivegrowthofthesesecondarymarkets（whoselevelsofactivitynowfrequentlyexceedtheun-derlyingmarketsonwhichtheirproductsarebased）continuesunabated,withtotaltradingvolumenowmeasuredinTrillionsofdollars.Thevari-etyandcomplexityofnewfinancialinstrumentsisoftenbewildering,andmucheffortgoesintotheanalysisofthe（evermorecomplex）mathematicalmodelsonwhichtheirexistenceispredicated.
