金融中的概率与随机过程导论（英文版——fabio trojani）

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1、IntroductiontoProbabilityTheoryandStochasticProcessesforFinance∗LectureNotesFabioTrojaniDepartmentofEconomics,UniversityofSt.Gallen,Switzerland∗Correspondenceaddress:FabioTrojani,SwissInstituteofBankingandFinance,UniversityofSt.Gallen,Rosenbergstr.52,CH-9000St.Gallen,e-mail:Fabio.Trojani@unisg

2、.ch.Contents1IntroductiontoProbabilityTheory41.1TheBinomialModel...................................41.1.1TheRiskyAsset.................................41.1.2TheRisklessAsset................................41.1.3ABasicNoArbitrageCondition........................51.1.4SomeBasicRemarks...........

3、....................51.1.5PricingDerivatives:afirstExample......................51.2FiniteProbabilitySpaces................................71.2.1MeasurableSpaces................................71.2.2Probabilitymeasures...............................111.2.3RandomVariables........................

4、........141.2.4ExpectedValueofRandomVariablesDefinedonFiniteMeasurableSpaces151.2.5ExamplesofProbabilitySpacesandRandomVariableswithFiniteSampleSpace.......................................161.3GeneralProbabilitySpaces...............................171.3.1SomeFirstExamplesofProbabilitySpaceswith

5、nonfiniteSampleSpaces.181.3.2ContinuityPropertiesofProbabilityMeasures................201.3.3RandomVariables................................211.3.4ExpectedValueandLebesgueIntegral.....................251.3.5SomeFurtherExamplesofProbabilitySpaceswithuncountableSampleSpaces281.4StochasticIndepend

6、ence.................................292ConditionalExpectationsandMartingales332.1TheBinomialModelOnceMore............................332.2SubSigmaAlgebrasand(Partial)Information....................3412.3ConditionalExpectations................................362.3.1Motivation..................

7、..................362.3.2DefinitionandProperties............................372.4MartingaleProcesses...................................413PricingPrinciplesintheAbsenceofArbitrage443.1StockPrices,RiskNeutralProbabilityMeasuresandMartingal