Predictive Modeling Applications in Actuarial Science: Volume 1, Predictive Modeling Techniques

563 Pages·2014·8.3 MB·English

by  Edward W. Frees

PredictiveModelingApplicationsinActuarialScience
VolumeI:PredictiveModelingTechniques
Predictive modeling involves the use of data to forecast future events. It relies on
capturing relationships between explanatory variables and the predicted variables
from past occurrences and exploiting these relationships to predict future outcomes.
Forecastingfuturefinancialeventsisacoreactuarialskill–actuariesroutinelyapply
predictivemodelingtechniquesininsuranceandotherriskmanagementapplications.
This book is for actuaries and other financial analysts who are developing their
expertiseinstatisticsandwishtobecomefamiliarwithconcreteexamplesofpredictive
modeling. The book also addresses the needs of more seasoned practicing analysts
whowouldlikeanoverviewofadvancedstatisticaltopicsthatareparticularlyrelevant
inactuarialpractice.
PredictiveModelingApplicationsinActuarialScienceemphasizeslife-longlearn-
ing by developing tools in an insurance context, providing the relevant actuarial
applications, and introducing advanced statistical techniques that can be used by
analyststogainacompetitiveadvantageinsituationswithcomplexdata.
Edward W. Frees is the Hickman-Larson Professor of Actuarial Science at the
WisconsinSchoolofBusiness,UniversityofWisconsin-Madison.
Richard A. Derrig is the president of Opal Consulting LLC and a visiting professor
of Risk, Insurance, and Healthcare Management at Fox School of Business, Temple
University.
GlennMeyershasrecentlyretiredasvicepresidentandchiefactuaryatISOInnovative
Analytics.

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
takingcoursesinorrelatedtoactuarialscience,aswellasmoreadvancedworksdesignedfor
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
NonlifeActuarialModels
Yiu-KuenTse
GeneralizedLinearModelsforInsuranceData
PietDeJong&GillianZ.Heller

PREDICTIVE MODELING
APPLICATIONS IN ACTUARIAL
SCIENCE
Volume I: Predictive Modeling Techniques
Editedby
EDWARD W. FREES
UniversityofWisconsin,Madison
RICHARD A. DERRIG
OpalConsultingLLC,Providence,RhodeIsland
GLENN MEYERS
ISOInnovativeAnalytics,JerseyCity,NewJersey
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learning,andresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107029873
©CambridgeUniversityPress2014
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2014
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
Predictivemodelingapplicationsinactuarialscience/[editedby]EdwardW.Frees,University
ofWisconsin,Madison,RichardA.Derrig,OpalConsultingLLC,GlennMeyers,
ISOInnovativeAnalytics,JerseyCity,NewJersey.
volumescm.–(Internationalseriesonactuarialscience)
Includesbibliographicalreferencesandindex.
Contents:volume1.Predictivemodelingtechniques
ISBN978-1-107-02987-3(v.1:hardback)
1.Actuarialscience. 2.Insurance–Mathematicalmodels. 3.Forecasting–Mathematicalmodels.
I.Frees,EdwardW. II.Derrig,RichardA. III.Meyers,Glenn.
HG8781.P74 2014
368(cid:2).01–dc23 2013049070
ISBN978-1-107-02987-3Hardback
Additionalresourcesforthispublicationathttp://research.bus.wisc.edu/PredModelActuaries
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLsforexternalorthird-party
Internetwebsitesreferredtointhispublicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwill
remain,accurateorappropriate.
Contents
ContributorList pagexiii
Acknowledgments xix
1 PredictiveModelinginActuarialScience 1
EdwardW.Frees,RichardA.Derrig,andGlennMeyers
1.1 Introduction 1
1.2 PredictiveModelingandInsuranceCompanyOperations 3
1.3 AShortHistoryofPredictiveModelinginActuarialScience 5
1.4 GoalsoftheSeries 8
References 9
I PredictiveModelingFoundations
2 OverviewofLinearModels 13
MarjorieRosenbergandJamesGuszcza
2.1 Introduction 13
2.2 LinearModelTheorywithExamples 15
2.3 CaseStudy 45
2.4 Conclusion 59
2.5 Exercises 60
References 63
3 RegressionwithCategoricalDependentVariables 65
MontserratGuille´n
3.1 CodingCategoricalVariables 65
3.2 ModelingaBinaryResponse 66
3.3 LogisticRegressionModel 67
3.4 ProbitandOtherBinaryRegressionModels 78
vii
15:59:22
viii Contents
3.5 ModelsforOrdinalCategoricalDependentVariables 79
3.6 ModelsforNominalCategoricalDependentVariables 81
3.7 FurtherReading 85
References 86
4 RegressionwithCount-DependentVariables 87
Jean-PhilippeBoucher
4.1 Introduction 87
4.2 PoissonDistribution 87
4.3 PoissonRegression 89
4.4 HeterogeneityintheDistribution 92
4.5 Zero-InflatedDistribution 102
4.6 Conclusion 105
4.7 FurtherReading 105
References 105
5 GeneralizedLinearModels 107
CurtisGaryDean
5.1 IntroductiontoGeneralizedLinearModels 107
5.2 ExponentialFamilyofDistributions 110
5.3 LinkFunctions 115
5.4 MaximumLikelihoodEstimation 118
5.5 GeneralizedLinearModelReview 121
5.6 Applications 122
5.7 ComparingModels 129
5.8 Conclusion 133
5.9 AppendixA.BinomialandGammaDistributionsin
ExponentialFamilyForm 133
5.10 AppendixB.CalculatingMeanandVariancefrom
ExponentialFamilyForm 135
References 136
6 FrequencyandSeverityModels 138
EdwardW.Frees
6.1 HowFrequencyAugmentsSeverityInformation 138
6.2 SamplingandtheGeneralizedLinearModel 140
6.3 Frequency-SeverityModels 148
6.4 Application:MassachusettsAutomobileClaims 152
6.5 FurtherReading 160
15:59:22
Contents ix
6.6 AppendixA.SampleAverageDistributioninLinear
ExponentialFamilies 161
6.7 AppendixB.Over-SamplingClaims 162
References 164
II PredictiveModelingMethods
7 LongitudinalandPanelDataModels 167
EdwardW.Frees
7.1 Introduction 167
7.2 LinearModels 172
7.3 NonlinearModels 176
7.4 AdditionalConsiderations 180
7.5 FurtherReading 181
References 181
8 LinearMixedModels 182
KatrienAntonioandYanweiZhang
8.1 MixedModelsinActuarialScience 182
8.2 LinearMixedModels 192
8.3 Examples 201
8.4 FurtherReadingandIllustrations 213
References 215
9 CredibilityandRegressionModeling 217
VytarasBrazauskas,HaraldDornheim,andPonmalarRatnam
9.1 Introduction 217
9.2 CredibilityandtheLMMFramework 220
9.3 NumericalExamples 224
9.4 TheoryversusPractice 227
9.5 FurtherReading 232
9.6 Appendix 233
References 234
10 Fat-TailedRegressionModels 236
PengShi
10.1 Introduction 236
10.2 Transformation 238
10.3 GLM 241
15:59:22
x Contents
10.4 RegressionwithGeneralizedDistributions 243
10.5 MedianRegression 250
10.6 AppendixA.TailMeasure 255
10.7 AppendixB.InformationMatrixforGB2Regression 256
References 258
11 SpatialModeling 260
EikeBrechmannandClaudiaCzado
11.1 Introduction 260
11.2 ExploratoryAnalysisofSpatialData 262
11.3 SpatialAutoregression 265
11.4 AverageClaimSizeModeling 269
11.5 HierarchicalModelforTotalLoss 273
11.6 DiscussionandConclusion 278
References 278
12 UnsupervisedLearning 280
LouiseFrancis
12.1 Introduction 280
12.2 Datasets 283
12.3 FactorandPrincipalComponentsAnalysis 285
12.4 ClusterAnalysis 294
12.5 Exercises 309
References 310
III BayesianandMixedModeling
13 BayesianComputationalMethods 315
BrianHartman
13.1 WhyBayesian? 315
13.2 PersonalAutomobileClaimsModeling 316
13.3 BasicsofBayesianStatistics 316
13.4 ComputationalMethods 319
13.5 PriorDistributions 326
13.6 Conclusion 330
13.7 FurtherReading 330
References 331
14 BayesianRegressionModels 334
LuisE.Nieto-BarajasandEnriquedeAlba
14.1 Introduction 334
15:59:22