gillam & snader, retro rating

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1、2014-CAS8§9Gillam&Snader,RetroRatingHCM5/13/14,Page522Section9,Gillam&Snader,Part2,RetrospectiveRating361OutlineofGillamandSnader:362Part1.ExperienceRatingPart2.RetrospectiveRatingPrefaceontheWorkersCompensationExpenseProgram363A.SpecificationsofthePlan1.TheFormulaforRetrospecti

2、vePremiumAGeneralConvention2.EntryRatios3.TheBasicPremium4.TheInsuranceCharge5.Expenses6.TheTaxMultiplier7.TheBalanceEquations8.TableMB.InsuranceChargeReflectingLossLimitations(ICRLL)C.SimplifiedConstructionofTableM3641.Construction2.InsuranceChargeandSavings3.SummaryD.Illustrat

3、ions1.SelectedLossRatioExample2.ASpecialCase,MinimumEqualsBasicE.AggregateBalanceF.SummaryG.ExcessPurePremiumRatios,FormalDefinition1.Definition2.TheContinuousCase365Part3.RelatedTopicsMoreimportantsectionsanditemsinbold.Lessimportantsectionsanditemsinitalics.361“FundamentalsofI

4、ndividualRiskRating”byWilliamR.GillamandRichardH.Snader.ForPart2,seeCASLearningObjectives:B2,B5,andB6362Parts1and3arecoveredinothersectionsofthisstudyguide.363Seealso“GoingfromaPurePremiumtoaRate,”byDavidB.Schofield,formerlyontheExam5syllabus.364TrytolearnthismaterialonConstruct

5、ingTableMfirstfromthesyllabusreadingbyBrosius.365SeealsothesyllabusreadingsbySkurnickandLee.2014-CAS8§9Gillam&Snader,RetroRatingHCM5/13/14,Page523FormulasandIdeas,Gillam&Snader,RetrospectiveRating:H≤R=(b+cL)T≤G,whereR=theretrospectivepremium.b=thebasicpremium=basicpremiumfactort

6、imesstandardpremium.c=thelossconversionfactorforexpenseswhichvarywithloss.L=actuallossesincurredsubjecttoanyapplicablelimitation.T=theTaxMultiplier.366H=theminimumretrospectivepremium.G=themaximumretrospectivepremium.E=expectedlosses.Entryratio=r=L/E.G=(b+crGE)T.H=(b+crHE)T.then

7、etinsurancecharge=I=(XG-SH)E,where∞∞XG=chargeatrG=∫(r−rG)f(r)dr=∫{1-F(r)}dr.rrGGrHrHSH=savingsatrH=∫(rH−r)f(r)dr=∫F(r)dr.00Thebasicpremium=b=e-(c-1)E+cI=e-(c-1)E+c(XG-SH)E.1-DExpenses=e=-E,TwhereDisthepremiumdiscount.Guaranteedcostpremium=T(e+E)=1-D.0.2+E(1+µ)1TheTaxMultipl

8、ier=T=,where0.2+E1−τE=permissiblelossratio,τ=pr