保险和金融用的例外事件模型

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作　者：	（）Paul Embrechts等著
出版社：	世界图书出版公司北京公司
丛编项：	Applications of Mathematics
标　签：	经济数学

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ISBN：	9787506259293	出版时间：	2003-01-01	包装：	胶版纸
开本：	22cm	页数：	648页	字数：

内容简介

　　In a recent issue， The New Scientist ran a cover story under the title： "Mission improbable. How to predict the unpredictable"; see Matthews [448]. In it， the author describes a group of mathematicians who claim that extreme value theory （EVT） is capable of doing just that： predicting the occurrence of rare events， outside the range of available data. All members of this group， the three of us included， would immediately react with： "Yes， but， ..."， or， "Be aware...". Rather than at this point trying to explain what EVT can and cannot do， we would like to quote two members of the group referred to in [448]. Richard Smith said， "There is always going to be an element of doubt， as one is extrapolating into areas one doesn't know about. But what EVT is doing is making the best use of whatever data you have about extreme phenomena." Quoting from Jonathan Tawn， "The key message .is that EVT cannot do magic - but it can do a whole lot better than empirical curvefitting and guesswork. My answer to the sceptics is that if people aren't given well-founded methods like EVT， they'll just use dubious ones instead."此书为英文版。

作者简介

暂缺《保险和金融用的例外事件模型》作者简介

图书目录

ReaderGuidelines
1RiskTheory
1.1TheRuinProblem
1.2TheCramer-LundbergEstimate
1.3RuinTheoryforHeavy-TailedDistributions
1.3.1SomePreliminaryResults
1.3.2Cramer-LundbergTheoryforSubexponentialDistributions
1.3.3TheTotalClaimAmountintheSubexponentialCase
1.4Cramer-LundbergTheoryforLargeClaims:aDiscussion
1.4.1SomeRelatedClassesofHeavy-TailedDistributions
1.4.2TheHeavy-TailedCramer-LundbergCaseRevisited
2FluctuationsofSums
2.1TheLawsofLargeNumbers
2.2TheCentralLimitProblem
2.3RefinementsoftheCLT
2.4TheFunctionalCLT:BrownianMotionAppears
2.5RandomSums
2.5.1GeneralRandomlyIndexedSequences
2.5.2RenewalCountingProcesses
2.5.3RandomSumsDrivenbyRenewalCountingProcesses
3FluctuationsofMaxima
3.1LimitProbabilitiesforMaxima
3.2WeakConvergenceofMaximaUnderAffineTransformations
3.3MaximumDomainsofAttractionandNormingConstants
3.3.1TheMaximumDomainofAttractionoftheFrechetDistribution(x)=exp{-x-a}
3.3.2TheMaximumDomainofAttractionoftheWeibullDistribution(x)=exp{-(-x)a}
3.3.3TheMaximumDomainofAttractionoftheGumbelDistributionA(x)=exp{-exp{-x}}
3.4TheGeneralisedExtremeValueDistributionandtheGeneralisedParetoDistribution
3.5AlmostSureBehaviourofMaxima
4FluctuationsofUpperOrderStatistics
4.1OrderStatistics
4.2TheLimitDistributionofUpperOrderStatistics
4.3TheLimitDistributionofRandomlyIndexedUpperOrderStatistics
4.4SomeExtremeValueTheoryforStationarySequences
5AnApproachtoExtremesviaPointProcesses
5.1BasicFactsAboutPointProcesses
5.1.1DefinitionandExamples
5.1.2DistributionandLaplaceFunctional
5.1.3PoissonRandomMeasures
5.2WeakConvergenceofPointProcesses
5.3PointProcessesofExceedances
5.3.1TheIIDCase
5.3.2TheStationaryCase
5.4ApplicationsofPointProcessMethodstoIIDSequences
5.4.1RecordsandRecordTimes
5.4.2EmbeddingMaximainExtremalProcesses
5.4.3TheFrequencyofRecordsandtheGrowthofRecordTimes
5.4.4InvariancePrincipleforMaxima
5.5SomeExtremeValueTheoryforLinearProcesses
5.5.1NoiseintheMaximumDomainofAttractionoftheFrechetDistributiona
5.5.2SubexponentiaiNoiseintheMaximumDomainofAttractionoftheGumbelDistributionA
6StatisticalMethodsforExtremalEvents
6.1Introduction
6.2ExploratoryDataAnalysisforExtremes
6.2.1ProbabilityandQuantilePlots
6.2.2TheMeanExcessFunction
6.2.3Gumbel'sMethodofExceedances
6.2.4TheReturnPeriod
6.2.5RecordsasanExploratoryTool
6.2.6TheRatioofMaximumandSum
6.3ParameterEstimationfortheGeneralisedExtremeValueDistribution
6.3.1MaximumLikelihoodEstimation
6.3.2MethodofProbability-WeightedMoments
6.3.3TailandQuantileEstimation,aFirstGo
6.4EstimatingUnderMaximumDomainofAttractionConditions
6.4.1Introduction
6.4.2EstimatingtheShapeParameter
6.4.3EstimatingtheNormingConstants
6.4.4TailandQuantileEstimation
6.5FittingExcessesOveraThreshold
6.5.1FittingtheGPD
6.5.2AnApplicationtoRealData
7TimeSeriesAnalysisforHeavy-TailedProcesses
7.1AShortIntroductiontoClassicalTimeSeriesAnalysis
7.2Heavy-TailedTimeSeries
7.3EstimationoftheAutocorrelationFunction
7.4EstimationofthePowerTransferFunction
7.5ParameterEstimationforARMAProcesses
7.6SomeRemarksAboutNon-LinearHeavy-TailedModels
8SpecialTopics
8.1TheExtremalIndex
8.1.1DefinitionandElementaryProperties
8.1.2InterpretationandEstimationoftheExtremalIndex
8.1.3EstimatingtheExtremalIndexfromData
8.2ALargeClaimIndex
8.2.1TheProblem
8.2.2TheIndex
8.2.3SomeExamples
8.2.4OnSumsandExtremes
8.3WhenandHowRuinOccurs
8.3.1Introduction
8.3.2TheCramer-LundbergCase
8.3.3TheLargeClaimCase
8.4PerpetuitiesandARCHProcesses
8.4.1StochasticRecurrenceEquationsandPerpetuities
8.4.2BasicPropertiesofARCHProcesses
8.4.3ExtremesofARCHProcesses
8.5OntheLongestSuccess-Run
8.5.1TheTotalVariationDistancetoaPoissonDistribution
8.5.2TheAlmostSureBehaviour
8.5.3TheDistributionalBehaviour
8.6SomeResultsonLargeDeviations
8.7ReinsuranceTreaties
8.7.1Introduction
8.7.2ProbabilisticAnalysis
8.8StableProcesses
8.8.1StableRandomVectors
8.8.2SymmetricStableProcesses
8.8.3StableIntegrals
8.8.4Examples
8.9Self-Similarity
Appendix
A1ModesofConvergence
A1.1ConvergenceinDistribution
A1.2ConvergenceinProbability
A1.3AlmostSureConvergence
A1.4Lp-Convergence
A1.5ConvergencetoTypes
A1.6ConvergenceofGeneralisedInverseFunctions
A2WeakConvergenceinMetricSpaces
A2.1PreliminariesaboutStochasticProcesses
A2.2TheSpacesC[0,1]andD[0,1]
A2.3TheSkorokhodSpaceD(0,)
A2.4WeakConvergence
A2.5TheContinuousMappingTheorem
A2.6WeakConvergenceofPointProcesses
A3RegularVariationandSubexponentiality
A3.1BasicResultsonRegularVariation
A3.2PropertiesofSubexponentialDistributions
A3.3TheTailBehaviourofWeightedSumsofHeavy-TailedRandomVariables
A4SomeRenewalTheory
References
Index
ListofAbbreviationsandSymbols