math5633&56334CGUIDE

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1、AnIntroductoryGuideintheConstructionofActuarialModels:APreparationfortheActuarialExamC/4MarcelB.FinanArkansasTechUniversitycAllRightsReservedPreliminaryDraftLastUpdatedJuly12,2013ToAminiiPrefaceThisisthefthofaseriesoflecturenotesintendedtohelpindividualstopassactuarialexams.Thetopicsint

2、hismanuscriptparallelthetopicstestedonExamCoftheSocietyofActuariesexamsequence.Aswiththepreviousmanuscripts,themainobjectiveofthepresentmanuscriptistoincreaseusers'understandingofthetopicscoveredontheexam.The owoftopicsfollowsverycloselythatofKlugmanetal.LossModels:FromDatatoDecisions.Th

3、electurescoverdesignatedsectionsfromthisbookassuggestedbythe2013SOASyllabus.Therecommendedapproachforusingthismanuscriptistoreadeachsec-tion,workontheembeddedexamples,andthentryALLtheproblemsgiveninthetext.Ananswerkeyisprovidedbyrequest.Email:mnan@atu.edu.Thisworkhasbeensupportedbyarese

4、archgrantfromArkansasTechUni-versity.ProblemstakenfrompreviousSOA/CASexamswillbeindicatedbythesymbolz:Thismanuscriptcanbeusedforpersonaluseorclassuse,butnotforcom-mercialpurposes.Ifyoundanyerrors,Iwouldappreciatehearingfromyou:mnan@atu.eduMarcelB.FinanRussellville,ArkansasFebruary15,20

5、13.iiiivContentsPrefaceiiiActuarialModeling11UnderstandingActuarialModels..................2AReviewofProbabilityRelatedResults52ABriefReviewofProbability....................63AReviewofRandomVariables...................184RawandCentralMoments.....................345EmpiricalModels,Excessa

6、ndLimitedLossvariables.......456Median,Mode,Percentiles,andQuantiles.............627SumofRandomVariablesandtheCentralLimitTheorem....698MomentGeneratingFunctionsandProbabilityGeneratingFunc-tions................................78TailWeightofaDistribution879TailWeightMeasures:Momentsandth

7、eSpeedofDecayofS(x)8810TailWeightMeasures:HazardRateFunctionandMeanExcessLossFunction...........................9511EquilibriumDistributionsandtailWeight............102RiskMeasures10912CoherentRiskMeasurement....................11013Value-at-Risk..........................