随机分析基础
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作者[丹麦]麦考斯基 著
出版社世界图书出版公司
出版时间2009-08
版次1
装帧平装
上书时间2024-07-14
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图书标准信息
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作者
[丹麦]麦考斯基 著
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出版社
世界图书出版公司
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出版时间
2009-08
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版次
1
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ISBN
9787510005244
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定价
28.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
212页
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正文语种
英语
- 【内容简介】
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Iknewbetter.Atthattime.staftmembersofeconomicsandmathematicsdepartmentsalreadydiscussedtheuseoftheBlackandScholesoptionpricingformula;coursesonstochasticfinancewere0fieredatleadinginstitutionssuchasETHZfirich.ColumbiaandStanford;andthereWasageneralagreementthatnotonlystudentsandstaftmembersofeconomicsandmathematicsde-partments、butalsopractitionersinfinanciaiinstitutionsshouldknowmoreaboutthisnewtopic.
SoonIrealizedthatthereWasnotverymuchliteraturewhichcouldbeusedforteachingstochasticcaiculusataratherelementarylevel.Ialnfullyawareofthefactthatacombinationof“elementary”and“stochasticcalculus”isacontradictioniUitselfStochasticcalculusrequiresadvancedmathematicaitechniques;thistheorycannotbefullvunderstoodifonedoesnotknowaboutthebasicsofmeasuretheory,functionalanalysisandthetheoryofstochasticprocessesHowever.Istronglybelievethataninterestedpersonwhoknowsaboutelementaryprobabilitytheoryandwhocanhandletherulesofinte-grationanddifierentiationisabletounderstandthemainideasofstochasticcalculus.ThisissupportedbymyexperiencewhichIgainedincoursesforeconomicsstatisticsandmathematicsstudentsatVUWWellingtonandtheDepartmentofMathematicsinGroningen.IgotthesameimpressionasalecturerofcrashcoursesonstochasticcalculusattheSummerSchOOl.
- 【目录】
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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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