Workers Compensation Excess Ratios_An Alternative Method of Estimation英文学习材料

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1、WORKERSCOMPENSATIONEXCESSRATIOS:ANALTERNATIVEMETHODOFESTIMATIONHOWARDC.MAHLERAbstractThispaperpresentsanalternativemethodofcalcu-latingexcessratiosforworkerscompensationinsurance.Whilethemethodsharesmanysimilaritieswiththatpre-sentedbyGillam[1],thereareimportantdifferencesinapproach.The(adj

2、usted)dataisreliedupondirectlyforlowerlimits.ForhigherlimitsthisissupplementedbyamixedPareto-exponentialdistributionfittedtothe(ad-justed)data.1.INTRODUCTIONTheexcessratioforalimitLisdefinedastheratiooflossesexcessofLtothetotalground-uplosses.Iff(x)istheprobabilitydensityfunctionforthesizeo

3、flossdistribution,thentheexcessratioisdefinedas:!!L(x"L)f(x)dxR(L)=!!:0xf(x)dxTheexcessratiocanalsobewrittenintermsofthelimitedexpectedvalueE[X;L]andthemeanE[X]:R(L)=1"E[X;L]=E[X].SeeforexampleHoggandKlugman[2].Theexcessratioisanimportantstatisticwithmanyapplica-tions.Forexample,itcanbeused

4、tocalculateexcesslossfactorsforworkerscompensationinsurance,asdiscussedinGillam[1].Generally,theexcesslossfactorforalimitistheproductofanexcessratioandapermissiblelossratiowiththepossibleaddi-tionofariskload.11Thesimilarexcesslossandallocatedexpensefactors(ELAFs)areforuseintheALAEoptionforr

5、etrospectiverating.Let1+abethefactortoloadlossesforallocatedlossadjustmentexpense.ThenforanaccidentlimitL,onecomputesR(L=(1+a))andmulti-132WORKERSCOMPENSATIONEXCESSRATIOS133Sinceexcesslossfactorsaretypicallycalculatedbyhazardgroupandaccidentlimit,excessratiosneedtobeestimatedbyhazardgroupan

6、dbyaccidentlimit.Thispaperwillshowonemethodofestimatingsuchexcessratios,withanemphasisongeneralprinciplesratherthanontheimportantdetailsthatmayaffecttheestimateinspecificsituations.2.DATAAsalways,thefirststepistocollecttheappropriatedata.AsinGillam[1],UnitStatisticalPlandataisusedatthird,fo

7、urth,andfifthreport.Allmedicalonlylossesareassumedtobebelowanyaccidentlimit.Forlosttimeclaims,theUnitStatisticalPlandatahastheindividualclaimsize2forthoseclaimsgreaterthan$2,000.(Thoseclaimsofsizelessthan$2,000maybereportedonagroupedbasis;alloftheirlosse