Predictive Modeling Applications in Actuarial Science, Volume 2: Case Studies in Insurance

334 Pages·2016·8.81 MB·English

by  Edward W. Frees

PredictiveModelingApplicationsinActuarialScience
VolumeII:CaseStudiesinInsurance
Predictive modeling uses data to forecast future events. It exploits relationships between
explanatoryvariablesandthepredictedvariablesfrompastoccurrencestopredictfutureout-
comes.Forecastingfinancialeventsisacoreskillthatactuariesroutinelyapplyininsurance
andotherrisk-managementapplications.PredictiveModelingApplicationsinActuarialSci-
enceemphasizeslifelonglearningbydevelopingtoolsinaninsurancecontext,providingthe
relevantactuarialapplications,andintroducingadvancedstatisticaltechniquesthatcanbe
usedtogainacompetitiveadvantageinsituationswithcomplexdata.
VolumeIIexaminesapplicationsofpredictivemodeling.WhereVolumeIdevelopedthe
foundationsofpredictivemodeling,VolumeIIexplorespracticalusesfortechniques,focus-
ingespeciallyonpropertyandcasualtyinsurance.Readersareexposedtoavarietyoftech-
niquesinconcrete,real-lifecontextsthatdemonstratetheirvalue,andtheoverallvalueof
predictivemodeling,forseasonedpracticinganalystsaswellasthosejuststartingout.
EdwardW.(Jed)FreesistheHickman-LarsonChairofActuarialScienceattheUniversity
of Wisconsin–Madison. He received his PhD in mathematical statistics in 1983 from the
UniversityofNorthCarolinaatChapelHillandisaFellowofboththeSocietyofActuaries
(SoA) and the American Statistical Association (the only Fellow of both organizations).
Regardinghisresearch,ProfessorFreeshaswonseveralawardsforthequalityofhiswork,
includingtheHalmstadPrizeforbestpaperpublishedintheactuarialliterature(fourtimes).
Glenn Meyers, PhD, FCAS, MAAA, CERA, retired from ISO at the end of 2011 after a
37-year career as an actuary. He holds a BS in mathematics and physics from Alma Col-
lege, an MA in mathematics from Oakland University, and a PhD in mathematics from
SUNYatAlbany.AfrequentspeakeratCasualtyActuarialSociety(CAS)meetings,hehas
served,andcontinuestoserve,theCASandtheInternationalActuarialAssociationonvari-
ousresearchandeducationcommittees.HehasalsoservedontheCASBoardofDirectors.
HehasseveralpublishedarticlesintheProceedingsoftheCasualtyActuarialSociety,Vari-
ance, and Actuarial Review. His research contributions have been recognized by the CAS
through his being a three-time winner of the Woodward-Fondiller Prize; a two-time win-
neroftheDorweilerPrize;andawinneroftheDFAPrize,theReservesPrize,theMatthew
RodermundServiceAward,andtheMichelbacherSignificantAchievementAward.Inretire-
ment,hestillspendssomeofhistimeonhiscontinuingpassionforactuarialresearch.
RichardA.DerrigisfounderandprincipalofOPALConsultingLLC,whichisafirmthat
provides research and regulatory support to property casualty insurance clients. Primary
areasofexpertiseincludefinancialpricingmodels,databaseanddata-miningdesign,fraud
detection planning and implementation, and expert testimony for regulation and litigation
purposes.

INTERNATIONAL SERIES ON ACTUARIAL SCIENCE
EditorialBoard
ChristopherDaykin(IndependentConsultantandActuary)
AngusMacdonald(Heriot-WattUniversity)
The International Series on Actuarial Science, published by Cambridge University Press in
conjunction with the Institute and Faculty of Actuaries, contains textbooks for students tak-
ing courses in or related to actuarial science, as well as more advanced works designed for
continuingprofessionaldevelopmentorfordescribingandsynthesizingresearch.Theseries
isavehicleforpublishingbooksthatreflectchangesanddevelopmentsinthecurriculum,that
encouragetheintroductionofcoursesonactuarialscienceinuniversities,andthatshowhow
actuarialsciencecanbeusedinallareaswherethereislong-termfinancialrisk.
Acompletelistofbooksintheseriescanbefoundatwww.cambridge.org/statistics.Recent
titlesincludethefollowing:
ComputationandModellinginInsuranceandFinance
ErikBølviken
SolutionsManualforActuarialMathematicsforLifeContingentRisks(2ndEdition)
DavidC.M.Dickson,MaryR.Hardy&HowardR.Waters
ActuarialMathematicsforLifeContingentRisks(2ndEdition)
DavidC.M.Dickson,MaryR.Hardy&HowardR.Waters
RiskModellinginGeneralInsurance
RogerJ.Gray&SusanM.Pitts
FinancialEnterpriseRiskManagement
PaulSweeting
RegressionModelingwithActuarialandFinancialApplications
EdwardW.Frees
PredictiveModelingApplicationsinActuarialScience,VolumeI:PredictiveModeling
Techniques
EditedbyEdwardW.Frees,RichardA.Derrig&GlennMeyers
NonlifeActuarialModels
Yiu-KuenTse
GeneralizedLinearModelsforInsuranceData
PietDeJong&GillianZ.Heller

PREDICTIVE MODELING
APPLICATIONS IN ACTUARIAL
SCIENCE
Volume II: Case Studies in Insurance
EDWARD W. FREES
UniversityofWisconsin–Madison
GLENN MEYERS
RICHARD A. DERRIG
OPALConsultingLLC
32AvenueoftheAmericas,NewYork,NY10013
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107029880
©CambridgeUniversityPress2016
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2016
PrintedintheUnitedStatesofAmericabySheridanBooks,Inc.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
ISBN978-1-107-02988-0Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain,
accurateorappropriate.
Contents
Contributors pagexi
Preface xv
Acknowledgments xix
1 PurePremiumModelingUsingGeneralizedLinearModels 1
ErnestoSchirmacher
1.1 Introduction 1
1.2 DataCharacteristics 3
1.3 ExploratoryDataAnalysis 6
1.4 FrequencyModeling 12
1.5 SeverityModeling 23
1.6 PurePremium 30
1.7 Validation 34
1.8 Conclusions 37
References 38
2 ApplyingGeneralizedLinearModelstoInsuranceData:
Frequency/SeverityversusPurePremiumModeling 39
DanTevet
2.1 Introduction 39
2.2 ComparingModelForms 40
2.3 TheDatasetandModelForms 44
2.4 Results 47
Appendix2.A ProofofEquivalencebetweenPure
PremiumModelForms 55
Conclusion 57
Appendix2.B TheGiniIndex 57
References 58
vii
viii Contents
3 GeneralizedLinearModelsasPredictiveClaimModels 60
GregTaylorandJamesSullivan
3.1 ReviewofLossReserving 60
3.2 AdditionalNotation 63
3.3 GLMBackground 64
3.4 AdvantagesofGLMs 66
3.5 Diagnostics 68
3.6 Example 73
3.7 Conclusion 97
References 98
4 FrameworksforGeneralInsuranceRatemaking:Beyondthe
GeneralizedLinearModel 100
PengShiandJamesGuszcza
4.1 Introduction 100
4.2 Data 102
4.3 UnivariateRatemakingFramework 104
4.4 MultivariateRatemakingFrameworks 113
4.5 ModelComparisons 122
4.6 Conclusion 123
References 124
5 UsingMultilevelModelingforGroupHealthInsuranceRatemaking:
ACaseStudyfromtheEgyptianMarket 126
MonaS.A.HammadandGalalA.H.Harby
5.1 MotivationandBackground 126
5.2 Data 130
5.3 MethodsandModels 141
5.4 Results 144
5.5 Conclusions 146
Acknowledgments 147
Appendix 147
References 157
6 ClusteringinGeneralInsurancePricing 159
JiYao
6.1 Introduction 159
6.2 OverviewofClustering 160
6.3 DatasetforCaseStudy 161
6.4 ClusteringMethods 163
6.5 Exposure-AdjustedHybrid(EAH)CluseringMethod 168
Contents ix
6.6 ResultsofCaseStudy 171
6.7 OtherConsiderations 177
6.8 Conclusions 178
References 179
7 ApplicationofTwoUnsupervisedLearningTechniquesto
QuestionableClaims:PRIDITandRandomForest 180
LouiseA.Francis
7.1 Introduction 180
7.2 UnsupervisedLearning 181
7.3 SimulatedAutomobilePIPQuestionableClaims
DataandtheFraudIssue 182
7.4 TheQuestionableClaimsDependentVariable
Problem 185
7.5 ThePRIDITMethod 185
7.6 ProcessingtheQuestionableClaimsDatafor
PRIDITAnalysis 187
7.7 ComputingRIDITSandPRIDITS 187
7.8 PRIDITResultsforSimulatedPIPQuestionable
ClaimsData 188
7.9 HowGoodIsthePRIDITScore? 189
7.10 TreesandRandomForests 192
7.11 UnsupervisedLearningwithRandomForest 194
7.12 SoftwareforRandomForestComputation 195
7.13 SomeFindingsfromtheBrockettetal.Study 201
7.14 RandomForestVisualizationviaMultidimensional
Scaling 202
7.15 KohonenNeuralNetworks 204
7.16 Summary 205
References 206
8 ThePredictiveDistributionofLossReserveEstimates
overaFiniteTimeHorizon 208
GlennMeyers
8.1 Introduction 208
8.2 TheCASLossReserveDatabase 210
8.3 TheCorrelatedChainLadderModel 212
8.4 ThePredictiveDistributionofFutureEstimates 213
8.5 TheImplicationsforCapitalManagement 216
8.6 SummaryandConclusions 223
References 223