Solutions Manual for Actuarial Mathematics for Life Contingent Risks

181 Pages·2012·0.78 MB·English

by  David C. M. Dickson

SolutionsManualforActuarialMathematicsforLifeContingentRisks
Thismust-havemanualprovidessolutionstoallexercisesinDickson,HardyandWaters’
ActuarialMathematicsforLifeContingentRisks,thegroundbreakingtextonthemodern
mathematicsoflifeinsurancethatistherequiredreadingfortheSOAExamMLCandalso
coversmoreorlessthewholesyllabusfortheUKSubjectCT5exam.Themorethan
150exercisesaredesignedtoteachskillsinsimulationandprojectionthroughcomputational
practice,andthesolutionsarewrittentogiveinsightaswellasexampreparation.Companion
spreadsheetsareavailableforfreedownloadtoshowimplementationofcomputational
methods.
DAVID C. M. DICKSON isAdjunctProfessorintheDepartmentofStatisticsand
ActuarialScienceattheUniversityofWaterloo.Hehastwicebeenawardedthe
H.M.JacksonPrizeoftheInstituteofActuariesofAustralia,mostrecentlyforhisbook
InsuranceRiskandRuin.
MARY R. HARDY holdstheCIBCChairinFinancialRiskManagementattheUniversity
ofWaterloo.ShehaswonawardsandcommendationsforherresearchfromtheInternational
ActuarialAssociation,theInstituteofActuariesandtheSocietyofActuaries.
HOWARD R. WATERS isaProfessorintheDepartmentofActuarialMathematicsand
StatisticsatHeriot-WattUniversity,Edinburgh.In2006hewasawardedtheFinlaisonMedal
bytheInstituteofActuariesfor“ServicestotheActuarialProfession”.
INTERNATIONAL SERIES ON ACTUARIAL SCIENCE
EditorialBoard
ChristopherDaykin(IndependentConsultantandActuary)
AngusMacdonald(Heriot-WattUniversity)
TheInternationalSeriesonActuarialScience,publishedbyCambridgeUniversityPressinconjunction
withtheInstituteandFacultyofActuaries,containstextbooksforstudentstakingcoursesinorrelatedto
actuarialscience,aswellasmoreadvancedworksdesignedforcontinuingprofessionaldevelopmentor
fordescribingandsynthesizingresearch.Theseriesisavehicleforpublishingbooksthatreflectchanges
anddevelopmentsinthecurriculum,thatencouragetheintroductionofcoursesonactuarialsciencein
universities,andthatshowhowactuarialsciencecanbeusedinallareaswherethereislong-termfinan-
cialrisk.
Acompletelistofbooksintheseriescanbefoundatwww.cambridge.org/statistics.Recenttitlesinclude
thefollowing:
RiskModellinginGeneralInsurance
RogerR.Gray&SusanM.Pitts
FinancialEnterpriseRiskManagement
PaulSweeting
RegressionModelingwithActuarialandFinancialApplications
EdwardW.Frees
ActuarialMathematicsforLifeContingentRisks
DavidC.M.Dickson,MaryR.Hardy&HowardR.Waters
NonlifeActuarialModels
Yiu-KuenTse
GeneralizedLinearModelsforInsuranceData
PietDeJong&GillianZ.Heller
Market-ValuationMethodsinLifeandPensionInsurance
ThomasMøller&MogensSteffensen
InsuranceRiskandRuin
DavidC.M.Dickson
SOLUTIONS MANUAL FOR
ACTUARIAL MATHEMATICS FOR
LIFE CONTINGENT RISKS
DAVID C. M. DICKSON
UniversityofWaterloo,Ontario
MARY R. HARDY
UniversityofWaterloo,Ontario
HOWARD R. WATERS
Heriot-WattUniversity,Edinburgh
CAMBRIDGE UNIVERSITY PRESS
Cambridge,NewYork,Melbourne,Madrid,CapeTown,
Singapore,SãoPaulo,Delhi,MexicoCity
CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB28RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107608443
(cid:2)c DavidC.M.Dickson,MaryR.HardyandHowardR.Waters2012
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2012
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
ISBN978-1-107-60844-3Paperback
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accuracyofURLsforexternalorthird-partyinternetwebsitesreferredtoin
thispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,
orwillremain,accurateorappropriate.
Contents
Preface pagevii
SolutionsforChapter1 1
SolutionsforChapter2 9
SolutionsforChapter3 18
SolutionsforChapter4 28
SolutionsforChapter5 40
SolutionsforChapter6 48
SolutionsforChapter7 60
SolutionsforChapter8 79
SolutionsforChapter9 101
SolutionsforChapter10 112
SolutionsforChapter11 124
SolutionsforChapter12 142
SolutionsforChapter13 154
SolutionsforChapter14 162
v

Preface
Thismanualpresentssolutionstoallexercisesfrom
ActuarialMathematicsforLifeContingentRisks(AMLCR),
byDavidC.M.Dickson,MaryR.Hardy,HowardR.Waters,
CambridgeUniversityPress,2009
ISBN9780521118255
It should be read in conjunction with the spreadsheets posted at the website
www.cambridge.org\9781107608443whichcontaindetailsofthecalculationsre-
quired.However,readersareencouragedtoconstructtheirownspreadsheetsbefore
lookingattheauthors’approach.Inthemanual,exercisesforwhichspreadsheetsare
postedareindicatedwithanE.
From time to time, updates to this manual may appear at www.cambridge.org\
9781107608443.
vii