金融中的数值方法和优化

图书标准信息

• 作者 [瑞士]吉利（M.Gilli） 著
• 出版社 世界图书出版公司
• 出版时间 2013-01
• 版次 1
• ISBN 9787510052651
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 584页
• 正文语种 英语

【内容简介】

　　《金融中的数值方法和优化》旨在为读者介绍金融计算工具―基本数值分析和计算技巧，如期权定价、并突出了模拟和优化的重要性，用许多章讲述投资组合保险和风险估计问题。特别地，有几章用于讲述优化探索和如何将他们应用于投资组合的选择、估值的校准和期权定价模型。这些具体的例子让读者学习了解决问题的具体步骤，以及将这些步骤举一反三。同时，这些应用使得《金融中的数值方法和优化》的参考价值大大提高。

【目录】

ListofAlgorithms
Acknowledgements
1.Introduction
1.1Aboutthisbook
1.2Principles
1.3onsoftware
1.4onapproximationsandaccuracy
1.5Summary：thethemeofthebook

PartOneFundamentals
2.Numericalanalysisinanutshell
2.1Computerarithmetic
Representationofrealnumbers
Machineprecision
Exampleoflimitationsoffloatingpointarithmetic
2.2Measuringerrors
2.3Approximatingderivativeswithfinitedifferences
Approximatingfirst-orderderivatives
Approximatingsecond-orderderivatives
Partialderivatives
Howtochooseh
Truncationerrorforforwarddifference
2.4Numericalinstabilityandill-conditioning
Exampleofanumericallyunstablealgorithm
Exampleofanill-conditionedproblem
2.5Conditionnumberofamatrix
Commentsandexamples
2.6Aprimeronalgorithmicandcomputationalcomplexity
2.6.1Criteriaforcomparison
Orderofcomplexityandclassification
2.AOperationcountforbasiclinearalgebraoperations
3.LinearequationsandLeastSquaresproblems
Choiceofmethod
3.1Directmethods
3.1.1Triangularsystems
3.1.2LUfactorization
3.1.3Choleskyfactorization
3.1.4QRdecomposition
3.1.5Singularvaluedecomposition
3.2Iterativemethods
3.2.1Jacobi，Gauss-Seidel，andSOR
Successiveoverrelaxation
3.2.2Convergenceofniterativemethods
3.2.3Generalstructureofalgorithmsforiterativemethods
3.2.4Blockiterativemethods
3.3Sparselinearsystems
3.3.1Tridiagonalsystems
3.3.2Irregularsparsematrices
3.3.3Structuralpropertiesofsparsematrices
3.4TheLeastSquaresproblem
3.4.1Methodofnormalequations
3.4.2LeastSquaresviaQRfactorization
3.4.3LeastSquaresviaSVDdecomposition
3.4.4Finalremarks
ThebackslashoperatorinMatlab
4.Finitedifferencemethods
4.1Anexampleofanumericalsolution
Afirstnumericalapproximation
Asecondnumericalapproximation
4.2Classificationofdifferentialequations
4.3TheBlack-Scholesequation
4.3.1Explicit，implicit，andθ-methods
4.3.2Initialandboundaryconditionsanddefinitionofthegrid
4.3.3Implementationoftheθ-methodwithMatlab
4.3.4Stability
4.3.5Coordinatetransformationofspacevariables
4.4Americanoptions
4.AAnoteonMatlab'sfunctionspdiags
5.Binomialtrees
5.1Motivation
Matchingmoments
5.2Growingthetree
5.2.1Implementingatree
5.2.2Vectorization
5.2.3Binomialexpansion
5.3Earlyexerase
5.4Dividends
5.5TheGreeks
Greeksfromthetree

PartTwoSimulation
6.Generatmgrandomnumbers
6.1MonteCarlomethodsandsampling
6.1.1Howitallbegan
6.1.2Financialapplications
6.2Uniformrandomnumbergenerators
6.2.1Congruentialgenerators
6.2.2MersenneTwister
6.3Nonuniformdistributions
6.3.1Theinversionmethod
6.3.2Acceptance-rejectionmethod
6.4Specializedmethodsforselecteddistributions
6.4.1Normaldistribution
6.4.2HigherordermomentsandtheCornish-Fisherexpansion
6.4.3Furtherdistributions
6.5Samplingfromadiscreteset
6.5.1Discreteuniformselection
6.5.2Roulettewheelselection
6.5.3Randompermutationsandshuffling
6.6Samplingerrors-andhowtoreducethem
6.6.1Thebasicproblem
6.6.2Quasi-MonteCarlo
6.6.3Stratifiedsampling
6.6.4Variancereduction
6.7Drawingfromempiricaldistributions
6.7.1Datarandomization
6.7.2Bootstrap
6.8Controlledexperimentsandexperimentaldesign
6.8.1Replicabilityandceterisparibusanalysis
6.8.2AvailablerandomnumbergeneratorsinMatlab
6.8.3UniformrandomnumbersfromMatlab'srandfunction
6.8.4GaussianrandomnumbersfromMatlab'srandnfunction
6.8.5Remedies
7.Modelingdependenaes
7.1Transformationmethods
7.1.1Linearcorrelation
7.1.2Rankcorrelation
7.2Markovchains
7.2.1Concepts
7.2.2TheMetropolisalgorithm
7.3Copulamodels
7.3.1Concepts
7.3.2Simulationusingcopulas
8.Agentleintroductiontofinancialsimulation
8.1Settingthestage
8.2Single-periodsimulations
8.2.1Terminalassetprices
8.2.2l-over-Nportfolios
8.2.3Europeanoptions
8.2.4VaRofacoveredputportfolio
8.3Simplepriceprocesses
8.4Processeswithmemoryinthelevelsofreturns
8.4.1Efficientversusadaptivemarkets
8.4.2Movingaverages
8.4.3Autoregressivemodels
8.4.4Autoregressivemovingaverage（ARMA）models
8.4.5SimulatingARMAmodels
8.4.6Modelswithlong-termmemory
8.5Time-varyingvolatility
8.5.1Theconcepts
8.5.2Autocorrelatedtime-varyingvolatility
8.5.3SimulatingGARCHprocesses
8.5.4Selectedfurtherautoregressivevolatilitymodels
8.6Adaptiveexpectationsandpatternsinpriceprocesses
8.6.1Price-earningsmodels
8.6.2Modelswithlearning
8.7Historicalsimulation
8.7.1Backtesting
8.7.2Bootstrap
8.8Agent-basedmodelsandcomplexity
9.Financialsimulationatwork：somecasestudies
9.1Constantproportionportfolioinsurance（CPPI）
9.1.1Basicconcepts
9.1.2Bootstrap
9.2VaRestimationwithExtremeValueTheory
9.2.1Basicconcepts
9.2.2Scalingthedata
9.2.3UsingExtremeValueTheory
9.3Optionpricing
9.3.1Modelingprices
9.3.2Pricingmodels
9.3.3Greeks
9.3.4Quasi-MonteCarlo
PartThreeOptimization