精算学：理论与方法（英文版）
出版时间:
2006-04
版次:
1
ISBN:
9787040192322
定价:
58.00
装帧:
精装
开本:
16开
纸张:
胶版纸
页数:
266页
正文语种:
英语
17人买过
-
SinceactuarialeducationwasintroducedintoChinain1980s,moreandmoreattentionhavebeenpaidtothetheoreticalandpracticalresearchofactuarialscienceinChina.
In1998,theNationalNaturalScienceFoundationofChinaapproveda1millionYuanRMBfinancialsupporttoakeyproject《InsuranceInformationProcessingandActuarialMathematicsTheory&Methodology》(project19831020),whichisthefirstkeyprojectonactuarialsciencesupportedbythegovernmentofChina.From1999to2003,professorsandexpertsfromFudanUniversity,PekingUniversity,InstituteofSoftwareofAcademiaSinica,EastChinaNormalUniversity,ShanghaiUniversityofFinanceandEconomics,ShanghaiUniversityandJinanUniversityworkedtogetherforthisproject,andachievedimportantsuccessesintheirresearchwork.Inasense,thisbookisasummationofwhattheyhadachieved.
Thebookconsistsofsevenchapters.Chapter1mainlypresentsthemajorresultsaboutruinprobabilities,thedistributionofsurplusbeforeandafterruinforacompoundPoissonmodelwithaconstantpremiumrateandaconstantinterestrate.Thischapteralsogivesasymptoticformulasofthelowandupperboundsforthedistributionofthesurplusimmediatelyafterruinundersubexponentialclaims.Chapter2introducessomerecentresultsoncompoundriskmodelsandcopuladecomposition.Forthecompoundriskmodels,itincludestherecursiveevaluationofcompoundriskmodelsonmixedtypeseveritydistributioninone-dimensionalcase,thebivariaterecursiveequationonexcess-of-lossreinsurance,andtheapproximationtototallossofhomogeneousindividualriskmodelbyacompoundPoissonrandomvariable.Onthecopuladecomposition,theuniquenessofbivariatecopulaconvexdecompositionisproved,whilethecoefficientofthetermsinthedecompositionequationisgiven.
Chapter3isconcernedwithdistortionpremiumprinciplesandsomerelatedtopics.Apartfromthecharacterizationofadistortionpremiumprinciple,thischapteralsoexaminestheadditivitiesinvolvedinpremiumpricingandrevealstherelationshipamongthethreetypesofadditivities.Furthermore,reductionofdistortionpremiumtostandarddeviationprincipleforcertaindistributionfamiliesisinvestigated.Inaddition,orderingproblemforreal-valuedrisks(beyondthenonnegativerisks)isaddressed,whichsuggeststhatitismorereasonabletoorderrisksinthedualtheorythantheoriginaltheory.
Chapter4illustratestheapplicationoffuzzymathematicsinevaluatingandanalyzingrisksforinsuranceindustry.Asanexample,fuzzycomprehensiveevaluationisusedtoevaluatetheriskofsufferingfromdiseasesrelatedtobetterlivingconditions.Fuzzyinformationprocessing(includinginformationdistributionandinformationdiffusion)isintroducedinthischapterandplaysanimportantroleindealingwiththesmallsampleproblem.Chapter5presentssomebasicdefinitionsandprinciplesofFuzzySetTheoryandthefuzzytoolsandtechniquesappliedtoactuarialscienceandinsurancepractice.Thefieldsofapplicationinvolveinsurancegame,insurancedecision,etc.Chapter6isconcernedwithsomeapplicationsoffinancialeconomicstoactuarialmathematics,especiallytolifeinsuranceandpension.Combiningfinancialeconomics,actuarialmathematicswithpartialdifferentialequation,ageneralframeworkhasbeenestablishedtostudythemathematicalmodelofthefairvaluationoflifeinsurancepolicyorpension.Inparticular,analyticsolutionsandnumericalresultshavebeenobtainedforvariouslifeinsurancepoliciesandpensionplans.Chapter7providesaworkingframeworkforexploringtheriskprofileandriskassessmentofChinainsurance.Itisfortheregulatoryobjectiveofbuildingarisk-orientedsupervisionsystembasedonChinainsurancemarketprofileandconsistenttotheinternationaldevelopmentofsolvencysupervision.
Theauthorsofvariouschaptersofthisbookare：ProfessorRongmingWangofEastChinaNormalUniversity(Chapter1),Dr.JingpingYangofPekingUniversity(Chapter2),Dr.XianyiWuofEastChinaNormalUniversity,Dr.XianZhouofHongKongUniversityandProfessorJinglongWangofEastChinaNormalUniversity(Chapter3),ProfessorHanjiShangofFudanUniversity(Chapter4),ProfessorYuchuLuofShanghaiUniversity(Chapter5),ProfessorWeixiShenofFudanUniversity(Chapter6)andProfessorZhigangXieofShanghaiUniversityofFinance&Economics(Chapter7).Astheeditor,Iammostgratefultoallauthorsfortheircooperation.IwouldliketothankProfessorTatsienLi,ProfessorZhongqinXuandProfessorWenlingZhang.Theirsupportisveryimportanttoourresearchworkandtothepublicationofthisbook.IalsothankMr.HaoWangforhiseffectiveworkineditingthebook. Preface
Chapter1RiskModelsandRuinTheory
1.1OntheDistributionofSurplusImmediatelyafterRuinunder InterestForce
1.1.1TheRiskModel
1.1.2EquationsforG(u,y)
1.1.2.1IntegralEquationsfor(u,y),G(u,y)and G(u,y)
1.1.2.2TheCase
1.1.3UpperandLowerBoundsforG(0,y)
1.2OntheDistributionofSurplusImmediatelybeforeRuinunderInterestForce
1.2.1EquationsforB(u,y)
1.2.1.1IntegralEquationsforB(u,y)
1.2.1.2TheCase＝0
1.2.1.3SolutionoftheIntegralEquation
1.2.2B(u,y)withZeroInitialReserve
1.2.3ExponentialClaimSize
1.2.4LundbergBound
1.3AsymptoticEstimatesoftheLowandUpperBoundsforthe
DistributionoftheSurplusImmediatelyafterRuinunder
SubexponentialClaims
1.3.1PreliminariesandAuxiliaryRelations
1.3.2AsymptoticEstimatesoftheLowandUpperBounds
1.4OntheRuinProbabilityunderaClassofRiskProcesses
1.4.1TheRiskModel
1.4.2TheLaplaceTransformoftheRuinProbabilitywithFiniteTime
1.4.3TwoCorollaries
Chapter2CompoundRiskModelsandCopulaDe-composition
2.1Introduction
2.2IndividualRiskModelandCompoundRiskModel
2.2.1TheLinkbetweentheCompoundRiskModelandtheIndividualRiskModel
2.2.2OneTheoremonExcess-of-lossReinsurance
2.3RecursiveCalculationofCompoundDistributions
2.3.1One-dimensionalRecursiveEquations
2.3.2ProofsofTheorems2.2-2.3
2.3.3BivariateRecursiveEquations
2.4TheCompoundPoissonRandomVariablesApproximationtotheIndividualRiskModel
2.4.1TheExistenceoftheOptimalPoissonr.v
2.4.2TheJointDistributionof(N(0),N)
2.4.3EvaluatingtheApproximationError
2.4.4TheApproximationtoFunctionsoftheTotalLoss
2.4.5TheUniquenessofthePoissonParametertoMinimiz-ingHn(0)
2.4.6Proofs
2.5BivariateCopulaDecomposition
2.5.1CopulaDecomposition
2.5.2ApplicationoftheCopulaDecomposition
Chapter3ComonotonicallyAdditivePremiumPrinciplesandSomeRelatedTopics
3.1Introduction
3.2CharacterizationofDistortionPremiumPrinciples
3.2.1Preliminaries
3.2.2GrecoTheorem
3.2.3CharacterizationofDistortionPremiumPrinciples
3.2.4FurtherRemarksonAdditivityofPremiumPrinciples
……
-
内容简介:
SinceactuarialeducationwasintroducedintoChinain1980s,moreandmoreattentionhavebeenpaidtothetheoreticalandpracticalresearchofactuarialscienceinChina.
In1998,theNationalNaturalScienceFoundationofChinaapproveda1millionYuanRMBfinancialsupporttoakeyproject《InsuranceInformationProcessingandActuarialMathematicsTheory&Methodology》(project19831020),whichisthefirstkeyprojectonactuarialsciencesupportedbythegovernmentofChina.From1999to2003,professorsandexpertsfromFudanUniversity,PekingUniversity,InstituteofSoftwareofAcademiaSinica,EastChinaNormalUniversity,ShanghaiUniversityofFinanceandEconomics,ShanghaiUniversityandJinanUniversityworkedtogetherforthisproject,andachievedimportantsuccessesintheirresearchwork.Inasense,thisbookisasummationofwhattheyhadachieved.
Thebookconsistsofsevenchapters.Chapter1mainlypresentsthemajorresultsaboutruinprobabilities,thedistributionofsurplusbeforeandafterruinforacompoundPoissonmodelwithaconstantpremiumrateandaconstantinterestrate.Thischapteralsogivesasymptoticformulasofthelowandupperboundsforthedistributionofthesurplusimmediatelyafterruinundersubexponentialclaims.Chapter2introducessomerecentresultsoncompoundriskmodelsandcopuladecomposition.Forthecompoundriskmodels,itincludestherecursiveevaluationofcompoundriskmodelsonmixedtypeseveritydistributioninone-dimensionalcase,thebivariaterecursiveequationonexcess-of-lossreinsurance,andtheapproximationtototallossofhomogeneousindividualriskmodelbyacompoundPoissonrandomvariable.Onthecopuladecomposition,theuniquenessofbivariatecopulaconvexdecompositionisproved,whilethecoefficientofthetermsinthedecompositionequationisgiven.
Chapter3isconcernedwithdistortionpremiumprinciplesandsomerelatedtopics.Apartfromthecharacterizationofadistortionpremiumprinciple,thischapteralsoexaminestheadditivitiesinvolvedinpremiumpricingandrevealstherelationshipamongthethreetypesofadditivities.Furthermore,reductionofdistortionpremiumtostandarddeviationprincipleforcertaindistributionfamiliesisinvestigated.Inaddition,orderingproblemforreal-valuedrisks(beyondthenonnegativerisks)isaddressed,whichsuggeststhatitismorereasonabletoorderrisksinthedualtheorythantheoriginaltheory.
Chapter4illustratestheapplicationoffuzzymathematicsinevaluatingandanalyzingrisksforinsuranceindustry.Asanexample,fuzzycomprehensiveevaluationisusedtoevaluatetheriskofsufferingfromdiseasesrelatedtobetterlivingconditions.Fuzzyinformationprocessing(includinginformationdistributionandinformationdiffusion)isintroducedinthischapterandplaysanimportantroleindealingwiththesmallsampleproblem.Chapter5presentssomebasicdefinitionsandprinciplesofFuzzySetTheoryandthefuzzytoolsandtechniquesappliedtoactuarialscienceandinsurancepractice.Thefieldsofapplicationinvolveinsurancegame,insurancedecision,etc.Chapter6isconcernedwithsomeapplicationsoffinancialeconomicstoactuarialmathematics,especiallytolifeinsuranceandpension.Combiningfinancialeconomics,actuarialmathematicswithpartialdifferentialequation,ageneralframeworkhasbeenestablishedtostudythemathematicalmodelofthefairvaluationoflifeinsurancepolicyorpension.Inparticular,analyticsolutionsandnumericalresultshavebeenobtainedforvariouslifeinsurancepoliciesandpensionplans.Chapter7providesaworkingframeworkforexploringtheriskprofileandriskassessmentofChinainsurance.Itisfortheregulatoryobjectiveofbuildingarisk-orientedsupervisionsystembasedonChinainsurancemarketprofileandconsistenttotheinternationaldevelopmentofsolvencysupervision.
Theauthorsofvariouschaptersofthisbookare：ProfessorRongmingWangofEastChinaNormalUniversity(Chapter1),Dr.JingpingYangofPekingUniversity(Chapter2),Dr.XianyiWuofEastChinaNormalUniversity,Dr.XianZhouofHongKongUniversityandProfessorJinglongWangofEastChinaNormalUniversity(Chapter3),ProfessorHanjiShangofFudanUniversity(Chapter4),ProfessorYuchuLuofShanghaiUniversity(Chapter5),ProfessorWeixiShenofFudanUniversity(Chapter6)andProfessorZhigangXieofShanghaiUniversityofFinance&Economics(Chapter7).Astheeditor,Iammostgratefultoallauthorsfortheircooperation.IwouldliketothankProfessorTatsienLi,ProfessorZhongqinXuandProfessorWenlingZhang.Theirsupportisveryimportanttoourresearchworkandtothepublicationofthisbook.IalsothankMr.HaoWangforhiseffectiveworkineditingthebook.
-
目录:
Preface
Chapter1RiskModelsandRuinTheory
1.1OntheDistributionofSurplusImmediatelyafterRuinunder InterestForce
1.1.1TheRiskModel
1.1.2EquationsforG(u,y)
1.1.2.1IntegralEquationsfor(u,y),G(u,y)and G(u,y)
1.1.2.2TheCase
1.1.3UpperandLowerBoundsforG(0,y)
1.2OntheDistributionofSurplusImmediatelybeforeRuinunderInterestForce
1.2.1EquationsforB(u,y)
1.2.1.1IntegralEquationsforB(u,y)
1.2.1.2TheCase＝0
1.2.1.3SolutionoftheIntegralEquation
1.2.2B(u,y)withZeroInitialReserve
1.2.3ExponentialClaimSize
1.2.4LundbergBound
1.3AsymptoticEstimatesoftheLowandUpperBoundsforthe
DistributionoftheSurplusImmediatelyafterRuinunder
SubexponentialClaims
1.3.1PreliminariesandAuxiliaryRelations
1.3.2AsymptoticEstimatesoftheLowandUpperBounds
1.4OntheRuinProbabilityunderaClassofRiskProcesses
1.4.1TheRiskModel
1.4.2TheLaplaceTransformoftheRuinProbabilitywithFiniteTime
1.4.3TwoCorollaries
Chapter2CompoundRiskModelsandCopulaDe-composition
2.1Introduction
2.2IndividualRiskModelandCompoundRiskModel
2.2.1TheLinkbetweentheCompoundRiskModelandtheIndividualRiskModel
2.2.2OneTheoremonExcess-of-lossReinsurance
2.3RecursiveCalculationofCompoundDistributions
2.3.1One-dimensionalRecursiveEquations
2.3.2ProofsofTheorems2.2-2.3
2.3.3BivariateRecursiveEquations
2.4TheCompoundPoissonRandomVariablesApproximationtotheIndividualRiskModel
2.4.1TheExistenceoftheOptimalPoissonr.v
2.4.2TheJointDistributionof(N(0),N)
2.4.3EvaluatingtheApproximationError
2.4.4TheApproximationtoFunctionsoftheTotalLoss
2.4.5TheUniquenessofthePoissonParametertoMinimiz-ingHn(0)
2.4.6Proofs
2.5BivariateCopulaDecomposition
2.5.1CopulaDecomposition
2.5.2ApplicationoftheCopulaDecomposition
Chapter3ComonotonicallyAdditivePremiumPrinciplesandSomeRelatedTopics
3.1Introduction
3.2CharacterizationofDistortionPremiumPrinciples
3.2.1Preliminaries
3.2.2GrecoTheorem
3.2.3CharacterizationofDistortionPremiumPrinciples
3.2.4FurtherRemarksonAdditivityofPremiumPrinciples
……
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