Applied Probability and Mathematical finance theory

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1、AppliedProbabilityandMathematicalFinanceTheoryHiroshiToyoizumi1January16,20061E-mail:toyoizumi@waseda.jpContents1Introduction52BasicProbabilityTheory62.1WhyProbability?............................62.2ProbabilitySpace............................62.3ConditionalProbabilityandIndependence.

2、..............82.4RandomVariables............................92.5Expectation,VarianceandStandardDeviation.............102.6CovarianceandCorrelation.......................122.7HowtoMakeaRandomVariable....................132.8References................................142.9Exercises......

3、..........................143NormalRandomVariables163.1WhatisNormalRandomVariable?...................163.2LognormalRandomVariables.....................173.3References................................203.4Exercises................................204UsefulProbabilityTheorems224.1TheLawofL

4、argeNumbers.......................224.2PoissonRandomVariablesandtheLawofSmallNumbers......234.3TheCentralLimitTheorem.......................234.4UsefulEstimations...........................244.5References................................274.6Exercises................................275B

5、rownianMotionsandPoissonProcesses285.1GeometricBrownianMotions.....................285.2DiscreteTimeTreeBinomialProcess.................305.3BrownianMotions...........................335.4PoissonProcesses............................365.5References................................375.6Ex

6、ercises................................372CONTENTS36SimulatingBrownianMotions386.1Mathematica..............................386.1.1AsanAdvancedCalculator..................386.2GeneratingRandomVariables.....................396.3Two-DimensionalBrownianMotions..................396.3.1Rando

7、mVariableonUnitCircle................396.3.2GeneratingBrownianMotion.................396.4GeometricBrownianMotions.....................416.4.1GeneratingBernouilliRandomVariables...........416.4.2Generatinggeometricbrownianmotions............417PresentValueAnalysis427.1InterestRates..