Springer.Mathematics.of.Financial.Markets.[1999.ISBN0387985530]

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1、MathematicsofFinancialMarketsRobertJ.ElliottP.EkkehardKoppSpringerContentsix9BondsandTermStructure2119.1MarketDynamics........................2119.2FuturePriceandFuturesContracts.............2159.3ChangingNum´eraire......................2199.4AGeneralOptionPricingFormula..........

2、....2229.5TermStructureModels....................2279.6DiffusionModelsfortheShort-TermRateProcess.....2299.7TheHeath–Jarrow–MortonModel..............2429.8AMarkovChainModel....................24710Consumption-InvestmentStrategies25110.1UtilityFunctions........................25110.

3、2AdmissibleStrategies......................25310.3UtilityMaximizationfromConsumption...........25810.4MaximizationofTerminalUtility...............26310.5UtilityMaximizationforBothConsumptionandTerminalWealth......................266References271Index289PrefaceThisworkisaimedatanau

4、diencewithasoundmathematicalbackgroundwishingtolearnabouttherapidlyexpandingfieldofmathematicalfinance.Itscontentissuitableparticularlyforgraduatestudentsinmathematicswhohaveabackgroundinmeasuretheoryandprobability.Theemphasisthroughoutisondevelopingthemathematicalconceptsre-quiredf

5、orthetheorywithinthecontextoftheirapplication.Noattemptismadetocoverthebewilderingvarietyofnovel(or‘exotic’)financialinstru-mentsthatnowappearonthederivativesmarkets;thefocusthroughoutremainsonarigorousdevelopmentofthemorebasicoptionsthatlieattheheartoftheremarkablerangeofcurrentap

6、plicationsofmartingaletheorytofinancialmarkets.Thefirstfivechapterspresentthetheoryinadiscrete-timeframework.Stochasticcalculusisnotrequired,andthismaterialshouldbeaccessibletoanyonefamiliarwithelementaryprobabilitytheoryandlinearalgebra.Thebasicideaofpricingbyarbitrage(or,rather,byn

7、onarbitrage)ispresentedinChapter1.TheuniquepriceforaEuropeanoptioninasingle-periodbinomialmodelisgivenandthenextendedtomulti-periodbinomialmodels.Chapter2introducestheideaofamartingalemeasureforpricepro-cesses.Followingadiscussionoftheuseofself-financingtradingstrategiestohedgeagai

8、nsttradingrisk,itisshownhowoption