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1、2014-CAS8§20Bernegger,ExposureCurvesHCM5/13/14,Page1197Section20,Bernegger,ExposureCurves&theMBBEFDDistributionClass837838Berneggerdiscussesaclassofdistributionsandhowtheycanbeusedtohelppricereinsurancetreaties.Heispricingexcessoflosspropertyreinsurance.839I
2、npropertyreinsurancethereisthepossibilityofatotallossoraMaximumPossibleLoss(MPL).Theinsurerretainsthelossinthelayerfrom0tod,whilethereinsurerpaysthelossexcessofd.Insteadthereinsurercouldjustbereinsuringalayerofloss.Berneggerisdiscussingexposureratingusingane
3、xposurecurve.840Mostofthepaperisspentonaparticularmathematicalformofexposurecurveandthecorrespondingdistributionfunction.LossEliminationRatiosandExcessRatios,Exam4Review:TheLossEliminationRatio(LER)isdefinedastheratioofthelosseseliminatedbyadeductibletotheto
4、tallossespriortoimpositionofthedeductible.Thelosseseliminatedbyadeductibled,areE[X∧d],theLimitedExpectedValueatd.841E[X∧x]LER(x)=.E[X]TheexcessratioR(x),isdefinedastheratiooflossdollarsexcessofxdividedbythetotallossdollars.ItisthecomplementoftheLossEliminati
5、onRatio;theysumtounity. E[X]-E[X∧x]E[X∧x]R(x)==1-=1-LER(x).E[X]E[X]Thepercentageoftotallossesinthelayerfromdtouis:LER(u)-LER(d)=R(d)-R(u). Foradistributionwithsupportstartingatzero,theLimitedExpectedValuecanbewrittenasanintegraloftheSurvivalFunctionfrom0tot
6、helimit:xE[X∧x]=∫S(t)dt.0837“SwissReExposureCurvesandtheMBBEFDDistributionClass,”byStefanBernegger,ASTINBulletin,Vol.27,No.1,May1997,pp.99-111.CASLearningObjectivesC3andC5. 838Addedtothesyllabusforthe2011exam.839Asdiscussedin“BasicsofReinsurancePricing”byDav
7、idR.Clark,“Propertyper-riskexcesstreatiesprovidealimitofcoverageinexcessofthecedingcompanyʼsretention.Thelayerappliesona“perrisk”basis,whichtypicallyreferstoasinglepropertylocation.Thisismorenarrowthana“peroccurrence”propertyexcesstreatywhichappliestomultipl
8、eriskstoprovidecatastropheprotection.”840Seepages16to18of“BasicsofReinsurancePricing,”byDavidR.Clark.841BerneggerusesthenotationL(d)forthelimitedexpectedvalueatd.OthersyllabusreadingsuseE[X;d].2
