随机分析基础
出版时间:
2009-08
版次:
1
ISBN:
9787510005244
定价:
28.00
装帧:
平装
开本:
24开
纸张:
胶版纸
页数:
212页
正文语种:
英语
-
Iknewbetter.Atthattime.staftmembersofeconomicsandmathematicsdepartmentsalreadydiscussedtheuseoftheBlackandScholesoptionpricingformula；coursesonstochasticfinancewere0fieredatleadinginstitutionssuchasETHZfirich.ColumbiaandStanford；andthereWasageneralagreementthatnotonlystudentsandstaftmembersofeconomicsandmathematicsde-partments、butalsopractitionersinfinanciaiinstitutionsshouldknowmoreaboutthisnewtopic.
SoonIrealizedthatthereWasnotverymuchliteraturewhichcouldbeusedforteachingstochasticcaiculusataratherelementarylevel.Ialnfullyawareofthefactthatacombinationof“elementary”and“stochasticcalculus”isacontradictioniUitselfStochasticcalculusrequiresadvancedmathematicaitechniques；thistheorycannotbefullvunderstoodifonedoesnotknowaboutthebasicsofmeasuretheory，functionalanalysisandthetheoryofstochasticprocessesHowever.Istronglybelievethataninterestedpersonwhoknowsaboutelementaryprobabilitytheoryandwhocanhandletherulesofinte-grationanddifierentiationisabletounderstandthemainideasofstochasticcalculus.ThisissupportedbymyexperiencewhichIgainedincoursesforeconomicsstatisticsandmathematicsstudentsatVUWWellingtonandtheDepartmentofMathematicsinGroningen.IgotthesameimpressionasalecturerofcrashcoursesonstochasticcalculusattheSummerSchOOl. ReaderGuidelines
1Preliminaries
1.1BasicConceptsflomProbabilityTheory
1.1.1RandomVariables
1.1.2RandomVectors
1.1.3IndependenceandDependence
1.2StochasticProcesses
1.3BrownianMotion
1.3.1DefiningProperties
1.3.2ProcessesDerivedfromBrownianMotion
1.3.3SimulationofBrownianSamplePaths
1.4ConditionalExpectation
1.4.1ConditionalExpectationunderDiscreteCondition
1.4.2Abouta-Fields
1.4.3TheGeneralConditionalExpectation
1.4.4RulesfortheCalculationofConditionalExpectations
1.4.5TheProjectionPropertyofConditionalExpectations
1.5Martingales
1.5.1DefiningProperties
1.5.2Examples
1.5.3TheInterpretationofaMartingaleasaFairGame
2TheStochasticIntegral
2.1TheRiemannandRiemann-StieltjesIntegrals
2.1.1TheOrdinaryRiemannIntegral
2.1.2TheRiemann-StieltjesIntegral
2.2TheItoIntegral
2.2.1AMotivatingExample
2.2.2TheItoStochasticIntegralforSimpleProcesses
2.2.3TheGeneralItoStochasticIntegral
2.3TheItoLemma
2.3.1TheClassicalChainRuleofDifferentiation
2.3.2ASimpleVersionoftheItoLemma
2.3.3ExtendedVersionsoftheItoLemma
2.4TheStratonovichandOtherIntegrals
3StochasticDifferentialEquations
3.1DeterministicDifferentialEquations
3.2ItoStochasticDifferentialEquations
3.2.1WhatisaStochasticDifferentialEquation?
3.2.2SolvingItoStochasticDifferentialEquationsbytheItoLemma
3.2.3SolvingItoDifferentialEquationsviaStratonovichCalculus
3.3TheGeneralLinearDifferentialEquation
3.3.1LinearEquationswithAdditiveNoise
3.3.2HomogeneousEquationswithMultiplicativeNoise
3.3.3TheGeneralCase
3.3.4TheExpectationandVarianceFunctionsoftheSolution
3.4NumericalSolution
3.4.1TheEulerApproximation
3.4.2TheMilsteinApproximation
4ApplicationsofStochasticCalculusinFinance
4.1TheBlack-ScholesOptionPricingFormula
4.1.1AShortExcursionintoFinance
4.1.2WhatisanOption?
4.1.3AMathematicalFormulationoftheOptionPricingProblem
4.1.4TheBlackandScholesFormula
4.2AUsefulTechnique:ChangeofMeasure
4.2.1WhatisaChangeoftheUnderlyingMeasure?
4.2.2AnInterpretationoftheBlack-ScholesFormulabyChangeofMeasure
Appendix
A1ModesofConvergence
A2Inequalities
A3Non-DifferentiabilityandUnboundedVariationofBrownianSamplePaths
A4ProofoftheExistenceoftheGeneralItoStochasticIntegral
A5TheRadon-NikodymTheorem
AoProofoftheExistenceandUniquenessoftheConditionalExpectation
Bibliography
Index
ListofAbbreviationsandSymbols
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内容简介:
Iknewbetter.Atthattime.staftmembersofeconomicsandmathematicsdepartmentsalreadydiscussedtheuseoftheBlackandScholesoptionpricingformula；coursesonstochasticfinancewere0fieredatleadinginstitutionssuchasETHZfirich.ColumbiaandStanford；andthereWasageneralagreementthatnotonlystudentsandstaftmembersofeconomicsandmathematicsde-partments、butalsopractitionersinfinanciaiinstitutionsshouldknowmoreaboutthisnewtopic.
SoonIrealizedthatthereWasnotverymuchliteraturewhichcouldbeusedforteachingstochasticcaiculusataratherelementarylevel.Ialnfullyawareofthefactthatacombinationof“elementary”and“stochasticcalculus”isacontradictioniUitselfStochasticcalculusrequiresadvancedmathematicaitechniques；thistheorycannotbefullvunderstoodifonedoesnotknowaboutthebasicsofmeasuretheory，functionalanalysisandthetheoryofstochasticprocessesHowever.Istronglybelievethataninterestedpersonwhoknowsaboutelementaryprobabilitytheoryandwhocanhandletherulesofinte-grationanddifierentiationisabletounderstandthemainideasofstochasticcalculus.ThisissupportedbymyexperiencewhichIgainedincoursesforeconomicsstatisticsandmathematicsstudentsatVUWWellingtonandtheDepartmentofMathematicsinGroningen.IgotthesameimpressionasalecturerofcrashcoursesonstochasticcalculusattheSummerSchOOl.
-
目录:
ReaderGuidelines
1Preliminaries
1.1BasicConceptsflomProbabilityTheory
1.1.1RandomVariables
1.1.2RandomVectors
1.1.3IndependenceandDependence
1.2StochasticProcesses
1.3BrownianMotion
1.3.1DefiningProperties
1.3.2ProcessesDerivedfromBrownianMotion
1.3.3SimulationofBrownianSamplePaths
1.4ConditionalExpectation
1.4.1ConditionalExpectationunderDiscreteCondition
1.4.2Abouta-Fields
1.4.3TheGeneralConditionalExpectation
1.4.4RulesfortheCalculationofConditionalExpectations
1.4.5TheProjectionPropertyofConditionalExpectations
1.5Martingales
1.5.1DefiningProperties
1.5.2Examples
1.5.3TheInterpretationofaMartingaleasaFairGame
2TheStochasticIntegral
2.1TheRiemannandRiemann-StieltjesIntegrals
2.1.1TheOrdinaryRiemannIntegral
2.1.2TheRiemann-StieltjesIntegral
2.2TheItoIntegral
2.2.1AMotivatingExample
2.2.2TheItoStochasticIntegralforSimpleProcesses
2.2.3TheGeneralItoStochasticIntegral
2.3TheItoLemma
2.3.1TheClassicalChainRuleofDifferentiation
2.3.2ASimpleVersionoftheItoLemma
2.3.3ExtendedVersionsoftheItoLemma
2.4TheStratonovichandOtherIntegrals
3StochasticDifferentialEquations
3.1DeterministicDifferentialEquations
3.2ItoStochasticDifferentialEquations
3.2.1WhatisaStochasticDifferentialEquation?
3.2.2SolvingItoStochasticDifferentialEquationsbytheItoLemma
3.2.3SolvingItoDifferentialEquationsviaStratonovichCalculus
3.3TheGeneralLinearDifferentialEquation
3.3.1LinearEquationswithAdditiveNoise
3.3.2HomogeneousEquationswithMultiplicativeNoise
3.3.3TheGeneralCase
3.3.4TheExpectationandVarianceFunctionsoftheSolution
3.4NumericalSolution
3.4.1TheEulerApproximation
3.4.2TheMilsteinApproximation
4ApplicationsofStochasticCalculusinFinance
4.1TheBlack-ScholesOptionPricingFormula
4.1.1AShortExcursionintoFinance
4.1.2WhatisanOption?
4.1.3AMathematicalFormulationoftheOptionPricingProblem
4.1.4TheBlackandScholesFormula
4.2AUsefulTechnique:ChangeofMeasure
4.2.1WhatisaChangeoftheUnderlyingMeasure?
4.2.2AnInterpretationoftheBlack-ScholesFormulabyChangeofMeasure
Appendix
A1ModesofConvergence
A2Inequalities
A3Non-DifferentiabilityandUnboundedVariationofBrownianSamplePaths
A4ProofoftheExistenceoftheGeneralItoStochasticIntegral
A5TheRadon-NikodymTheorem
AoProofoftheExistenceandUniquenessoftheConditionalExpectation
Bibliography
Index
ListofAbbreviationsandSymbols
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随机分析基础
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