Springer.Maths.&.Stats.Mathematics.of.Financial.Markets.1999.[Springer]

《Springer.Maths.&.Stats.Mathematics.of.Financial.Markets.1999.[Springer]》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。

1、MathematicsofFinancialMarketsRobertJ.ElliottP.EkkehardKoppSpringerPrefaceThisworkisaimedatanaudiencewithasoundmathematicalbackgroundwishingtolearnabouttherapidlyexpanding?eldofmathematical?nance.Itscontentissuitableparticularlyforgraduatestudentsinmathematic

2、swhohaveabackgroundinmeasuretheoryandprobability.Theemphasisthroughoutisondevelopingthemathematicalconceptsre-quiredforthetheorywithinthecontextoftheirapplication.Noattemptismadetocoverthebewilderingvarietyofnovel(or‘exotic’)?nancialinstru-mentsthatnowappear

3、onthederivativesmarkets;thefocusthroughoutremainsonarigorousdevelopmentofthemorebasicoptionsthatlieattheheartoftheremarkablerangeofcurrentapplicationsofmartingaletheoryto?nancialmarkets.The?rst?vechapterspresentthetheoryinadiscrete-timeframework.Stochasticca

4、lculusisnotrequired,andthismaterialshouldbeaccessibletoanyonefamiliarwithelementaryprobabilitytheoryandlinearalgebra.Thebasicideaofpricingbyarbitrage(or,rather,bynonarbitrage)ispresentedinChapter1.TheuniquepriceforaEuropeanoptioninasingle-periodbinomialmodel

5、isgivenandthenextendedtomulti-periodbinomialmodels.Chapter2introducestheideaofamartingalemeasureforpricepro-cesses.Followingadiscussionoftheuseofself-?nancingtradingstrategiestohedgeagainsttradingrisk,itisshownhowoptionscanbepricedusinganequivalentmeasurefor

6、whichthediscountedpriceprocessisamar-tingale.ThisisillustratedforthesimplebinomialCox–Ross–Rubinsteinpricingmodels,andtheBlack–Scholesformulaisderivedasthelimitofthepricesobtainedforsuchmodels.Chapter3givesthe‘fundamentalthe-oremofassetpricing’,whichstatesth

7、atifthemarketdoesnotcontainviPrefacearbitrageopportunitiesthereisanequivalentmartingalemeasure.Explicitconstructionsofsuchmeasuresaregiveninthesettingof?nitemarketmodels.CompletenessofmarketsisinvestigatedinChapter4;inacom-pletemarket,everycontingentclaimcan

8、begeneratedbyanadmissibleself-?nancingstrategy(andthemartingalemeasureisunique).Stoppingtimes,martingaleconvergenceresults,andAmericanoptionsarediscussedinadiscrete-timeframeworkinChapter5.These