随机分析基础

图书标准信息

• 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
• ISBN 9787510005244
• 定价 28.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 212页
• 正文语种 英语

【内容简介】

　　Iknewbetter.Atthattime.staftmembersofeconomicsandmathematicsdepartmentsalreadydiscussedtheuseoftheBlackandScholesoptionpricingformula；coursesonstochasticfinancewere0fieredatleadinginstitutionssuchasETHZfirich.ColumbiaandStanford；andthereWasageneralagreementthatnotonlystudentsandstaftmembersofeconomicsandmathematicsde-partments、butalsopractitionersinfinanciaiinstitutionsshouldknowmoreaboutthisnewtopic.
　　SoonIrealizedthatthereWasnotverymuchliteraturewhichcouldbeusedforteachingstochasticcaiculusataratherelementarylevel.Ialnfullyawareofthefactthatacombinationof“elementary”and“stochasticcalculus”isacontradictioniUitselfStochasticcalculusrequiresadvancedmathematicaitechniques；thistheorycannotbefullvunderstoodifonedoesnotknowaboutthebasicsofmeasuretheory，functionalanalysisandthetheoryofstochasticprocessesHowever.Istronglybelievethataninterestedpersonwhoknowsaboutelementaryprobabilitytheoryandwhocanhandletherulesofinte-grationanddifierentiationisabletounderstandthemainideasofstochasticcalculus.ThisissupportedbymyexperiencewhichIgainedincoursesforeconomicsstatisticsandmathematicsstudentsatVUWWellingtonandtheDepartmentofMathematicsinGroningen.IgotthesameimpressionasalecturerofcrashcoursesonstochasticcalculusattheSummerSchOOl.

【作者简介】

Thomas Mikosch，荷兰格罗宁根大学（英文：University of Groningen）教授。

                            

内容摘要

本书在没有应用深奥的数学理论的前提下全面阐述了金融随机微积分，减少了读者的学*担，并且该书没有讲述太多的测度论知识，而是给出了概率论的基本引入。书中列举了大量随机金融应用例子，特别是Black-Scholes期权价格公式的引入。本书可以作为非数学专业学生的随机微积分教程或者任何想学习随机金融的读者的入门教程。目次:基础；随机积分；随机微分方程；随机微积分在金融中的应用。

主编推荐

Thomas Mikosch，荷兰格罗宁根大学（英文：University of Groningen）教授。

                            

【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