miccolis, increased limit factors

《miccolis, increased limit factors》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、2014-CAS8§24MiccolisILFs,HCM5/13/14,Page1450Section24,Miccolis,IncreasedLimitFactors1169ThepaperbyMiccolisonILFsplustheimportantdiscussionbyRosenberghavebeenonthesyllabusforover3decades.Thus,therearelotsofpastexamquestions,andmostofwhatcanbeaskedhasbeenaskedatsomepointinthepast;ofcoursethereisalw

2、aysroomforsurprises.Knowtherelationofinflationandthefollowingitems:increasedlimitfactors,losseliminationratios,excess-of-lossreinsurancepurepremiums,trendfactorsbylayer.OutlineofMiccolis:1.ExpectedValuePricingE[X∧k]Formula4:I(k)=.E[X∧b]Formula6:Iʼ(k)=S(k)/E[X∧b]>0.Formula8:Iʼʼ(k)=-f(k)/E[X∧b]<0.

3、ConsistencyTest:TheILFsincreasewithlimitandareconcavedownwards.ExcessofLossCoverage:expectedpercentofbasiclimitlossesinalayerfromrtosis:I(s)-I(r).Trend:Afterinflationfactora,theILFinthelateryearis:I1(k)=I(k/a)/I(b/a).I(s/a)-I(r/a)E[X∧s/a]-E[X∧r/a]Theinflationinthelayerfromrtosis:a=a.I(s)-I(r)E[

4、X∧s]-E[X∧r]2.TheChargeforRiskE[(X∧L)]+λE[(X∧L)2]TheriskadjustedILFforlimitLis:,λissomeconstant.E[(X∧b)]+λE[(X∧b)2]3.Applications4.RelatedTopicsLeveragedEffectofInflationAggregateLimitsPerPerson,PerAccidentLimitsPropertyInsurance-CoinsurancePricing5.Conclusion1169“OntheTheoryofIncreasedLimitsan

5、dExcessofLossPricing,”byRobertS.Miccolis.PCASLXIV,1977,pp.27-59excluding“RiskReductionbyLayering”(pp.45-49).IncludingdiscussionofpaperbySheldonRosenberg,PCASLXIV,1977,pp.60-73.ThispaperhadjustbeenaddedtothesyllabuswhenItook(andpassed)Exam9in1979.CASLearningObjectiveB1.2014-CAS8§24MiccolisILFs,HCM

6、5/13/14,Page1451OutlineoftheDiscussionbyRosenberg:ConsistencyinIncreasedLimitsTablesExtensionto2DimensionalTables1.Themarginalrateshoulddecline(notincrease)alonganyrow.2.Themarginalrateshoulddecline(notincrease)downanycolumn.3.Comparingdifferencesalongeachoftwoadjacentrows,thecorrespondingdiffere

7、nceinthelowerrowshouldbelarger(notsmaller)thanthatinthehigherrow.4.Comparingdifferencesdowneachoftwoadjacentcolumns,thecorrespondingdifferenceintherighthandcolumnshouldbelarger(notsmaller)thanthatinthelefthandcolumn.An