mahler, discussion 1997 elfs

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1、2014-CAS8§15Mahler,Discussionof1997ELFsHCM5/13/14,Page923Section15,Mahler,Discussionof“Retro.Rating:1997ExcessLossFactors”643644ErrataforDiscussionbyHowardMahlerof“RetrospectiveRating:1997ExcessLossFactors”645^Atthebottomofpage320,theequationforR(100)isincorrect.Thisexampleofsimpledispersionisanexam

2、pleofamixturewithfivepieces.Theexcessratioofthemixtureisaweightedaverageofindividualexcessratios,withtheweightstheproductofthemeansandtheprobabilitiesforeachpieceofthemixture.646Iftheprobabilityofeachpieceofamixtureispi,Σpi=1,themeanofeachpieceofthemixtureis^mi,andRiistheexcessratioforeachpieceofth

3、emixture,thenR(L)=ΣpimiRi(L).Ifeachlossisdividedbyforexample.75,thenafterdevelopment,theexcessratioatListhesameastheoriginalexcessratioat0.75L.647Ri(L)istheexcessratiowhenthelosseshaveallbeendividedbyri.ThusRi(L)=R(riL).Intheexampleonpage320,eachmeanisproportionalto1/divisor=1/ri,andeachprobability

4、isthesameat1/5.Thustheweightsare:(1/5)(1/ri).Thesumoftheweightsis:Σ(1/5)(1/r648i)=(1/5)(1/0.75+1/0.833+1/1+1/1.25+1/1.5)=1.^ThusR(L)=Σ(1/5)(1/ri)R(riL)=(1/5)ΣR(riL)/ri.Therefore,thecorrectedequationatthebottomofpage320is:^R(100)=(1/5){R(75)/0.75+R(83.3)/0.833+R(100)/1+R(125)/1.25+R(150)/1.50}=(1/5)

5、{0.6009/0.75+0.5817/0.833+0.5582/1+0.5384/1.25+0.5191/1.50}=0.5669.643AppendixesB-Dareforreferenceonly.CandidatesdonotneedtomemorizeformulasinAppendicesB-D.CASLearningObjectiveB1.Thisreadingwasaddedtothesyllabusin2008.644TheoriginalpaperbyGillamandCouretinPCAS1997isnotonthesyllabus.ThediscussionbyM

6、ahlerinPCAS1998isonthesyllabus.645Official;foundbymelookingovermyownpaperadecadelater!ChecktheCASwebpageforanyupdates.646Seepage154of“WorkersCompensationExcessRatios:AnAlternateMethodofEstimation”byMahler.647Ifeachlossismultipliedby1/0.75=1.333,thisismathematicallythesameasuniforminflationof33.3%.Th

7、uswecangettheexcessratioafterdevelopment,bytakingtheoriginalexcessratioatthedeflatedvalueofL/1.333=0.75L.Increasingthesizesofloss,increasestheexcessratiooverafixedlimit.648Mahlerchosetheselossdivisors