金融用概率（－Patrick Roger）

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1、PATRICKROGERPROBABILITYFORFINANCEDOWNLOADFREETEXTBOOKSATBOOKBOON.COMNOREGISTRATIONNEEDEDProbabilityforFinancePatrickRogerStrasbourgUniversity,EMStrasbourgBusinessSchoolMay2010DownloadfreeebooksatBookBooN.com2ProbabilityforFinance©2010PatrickRoger&VentusPublishin

2、gApSISBN978-87-7681-589-9DownloadfreeebooksatBookBooN.com3ProbabilityforFinanceContentsContentsIntroduction81.Probabilityspacesandrandomvariables101.1Measurablespacesandprobabilitymeasures101.1.1σalgebra(ortribe)onasetΩ111.1.2Sub-tribesofA131.1.3Probabilitymeasu

3、res161.2ConditionalprobabilityandBayestheorem181.2.1Independanteventsandindependanttribes191.2.2Conditionalprobabilitymeasures211.2.3Bayestheorem241.3Randomvariablesandprobabilitydistributions251.3.1Randomvariablesandgeneratedtribes251.3.2Independantrandomvariab

4、les291.3.3Probabilitydistributionsandcumulativedistributions301.3.4Discreteandcontinuousrandomvariables341.3.5Transformationsofrandomvariables352.Momentsofarandomvariable372.1Mathematicalexpectation37what‘smissinginthisequation?YoucouldbeoneofourfuturetalentsPle

5、aseclicktheadvertmaeRsKinteRnationaLteChnoLogY&sCienCePRogRammeAreyouabouttograduateasanengineerorgeoscientist?Orhaveyoualreadygraduated?Ifso,theremaybeanexcitingfutureforyouwithA.P.Moller-Maersk.www.maersk.com/mitasDownloadfreeebooksatBookBooN.com4Probabilityfo

6、rFinanceContents2.1.1Expectationsofdiscreteandcontinousrandomvariables392.1.2Expectation:thegeneralcase402.1.3Illustration:Jensen’sinequalityandSaint-Peterburgparadox432.2Varianceandhighermoments462.2.1Second-ordermoments462.2.2Skewnessandkurtosis482.3Thevectors

7、paceofrandomvariables502.3.1Almostsurelyequalrandomvariables512.3.2ThespaceL1(Ω,A,P)532.3.3ThespaceL2(Ω,A,P)542.3.4Covarianceandcorrelation592.4EquivalentprobabilitiesandRadon-Nikodymderivatives632.4.1Intuition632.4.2RadonNikodymderivatives672.5Randomvectors692.

8、5.1Definitions692.5.2Applicationtoportfoliochoice713.Usualprobabilitydistributionsinfinancialmodels733.1Discretedistributions733.1.1Bernoullidistribution733.1.2Binomi