长寿风险管理研究综述

111(MacMinn,Brockett,Blake,2006;Stallard,2006)(IndividualLongevityRisk)12(AggregateLongevityRisk)(Milevsky,Promislow,Young,2006;Cairans,BlakeandDowd,2006a)BlakeBurrows(2001)(survivorbonds)(longevityderivatives)(Dowd,2003;Blake,2003;CowleyandCummins,2005;LinandCox,2005;Dowd,Blake,CairnsandDawson,2006;Blake,Cairns,DowdandMacMinn,2006)(mortalityprojection)234522.12.1.1CMIB1990(ContinuousMortalityInvestigationBureau)CMIB,1111()exp{}rrsrsiiriiiirGMxxxααα+−−−==+=+∑∑(2.1.1)0,2rs==(2.1.1)Gempertz1,2rs==(2.1.1)Makehamxqxmxµ(2.1.1)32.1.2HPHelligmanPollard(1980)Helligman-Pollard(HP)2()[ln()ln()]CxBExFxxxqADeGHp+−−=+⋅+(2.1.2)()CxBA+2[ln()ln()]ExFDe−−⋅xGHThatcher(1999)perksCarriere(1992)2.22.2.1Renshaw,HabermanHatzopolous(1996)(2.1.1)1958-90Sithole,HabermanS.VerrallR.J.(2000)1958-1994LegendreHP(Felipe,GuillenPerez-Marin(2002))2.2.2Lee-CarterLeeCarter(1992),,ln()xtxxtxtmabkε=++(2.2.1)xaxbxtk,xtε0εσ1xxβ=∑0ttκ=∑LeeCarter1900-1989ˆtkARIMA(0,1,0)ˆtktkLee-CarterLee-CarterBrouhnsDenuitVermun(2002),KoissiShapiroHögäns(2006),Lee(2000),RenshawHaberman(2003a,b),Wilmoth(1993)42.2.321Lee-Carter(2.2.1),,ln()log(,)xtxxtFxtµαε=++(2.2.2)log(,)xtFxtβκ=1log(,)0()ntttFxtx==∀∑RenshawandHaberman(2006)(0)(1)log(,)xtxxtFxtβτβκ−=+tx−txτ−(0)(1),,ln()xtxxtxxtxtµαβτβκε−=+++(2.2.3)RenshawandHaberman(2006)(0)1xxβ=∑(1)1xxβ=∑10ktxτ−=10tκ=(2.2.3)(1)0xβ=AC(age-cohort)(2.2.3)(0)0xβ=Lee-CarterRenshawandHaberman(2006)1961-2003Lee-CarterACLee-Carter2APC(age-period-cohort)APCholford(1983)APC3,,ln(/)xtxtxttxqpακγ−=++(2.2.4)xαtκtxγ−Debon,MartinezandMontes(2006)APCAPC2.2.4MilevskyPromislow(2001)Dahl(2004)DahlMǾller(2005)Biffis(2005)Cairns,BlakeDowd(2006a)MilevskyPromislow(2001)Dahl(2004)DahlMǾller(2005)Biffis(2005)Cairns,BlakeDowd(2006a)25Wong-fupuyHaberman(2004)3BlakeBurrows(2001)BlakeD(2003)Dowd(2003)BrownOrszag(2006)Turner(2006)MacMinn,BrockettBlake(2006)BlakeBurrows(2001)BlakeD(2003)Arrow-LindDowd(2003)BlakeBurrows(2001)Arrow-LindDowdDowdDowdDowdBlake(2003)DowdBrownOrszag(2006)BrownOrszagBrownOrszagBrownOrszagBrownOrszagTurner(2006)6MacMinn,BrockettBlake(2006)4MilevskPromislow(2001)(BlakeandBurrows,2001;CowleyandCummines,2005)HuangYangWangTsai(2007)Kim(2007)Blake,CairnsDowd(2006)CowleyandCummins(2005)4.14.1.13BlakeBurrows(2001)652000202020006585LinandCox(2005)(SpecialPurposeCompany,SPC)Bt3Dowd,Blake,CairnsandDawson(2006)“mortalitybonds”“survivorbonds”“longevitybonds”PBtVDt4.1.17DtFLinCox(2005)BtDtBlake,Cairns,DowdMacMinn(2006)tf()ttfSBlake,Cairns,DowdMacMinn12BlakeBurrows(2001)LinCox(2005)34()ttfStS(InverseFunction)()(1),0tttfSkSk=−5(tranche)Blake,CairnsDowd(2006)4.1.2LinandCox(2005)(SpecialPurposeCompany,SPC)xyBtDt4.1.1(counter-partyrisk)Dowd,Blake,CairnsandDawson(2006)Blake,CairnsDowd(2006)4.1.3Blake,CairnsDowd(2006)Blake,CairnsDowdxBtyDt4.1.28CME(ChicagoMercantileExchange)4.1.4Blake,CairnsDowd(2006)Cairns,BlakeDowd(2006b)4.24.2.1(Risk-Neutral)QPMilevskPromislow(2001)Dah(2004)DahlMǾller(2005)Biffis(2005)MiltersenPersson(2005)Cairns,BlakeDowd(2006a,2006b)0(LB)t(1,,tT=L)tStS0xtQ0001(LB)()TtQttVDES==Ω∑(4.2.1)0Ω00()QtESΩQtS0tDt0Cairns,BlakeDowd(2006b)EIB/BNPQ4.2.2(DistortionofDistribution)X()Fx()1()XXSxFx=−*()[()]SxgSx=(4.2.2)()g⋅(0)0g=(1)1g=()0gt′()0gt′′Wang(2000,2002)9—Wang()g⋅1()[()]guuαα−=ΦΦ+(4.2.3)()Φ⋅Wang(2000,2002)WangCAPMBlack-ScholesWangCAPMBlack-ScholesWang0xt(,)SxtLinCox(2005)WangDenuit,DevolderGoderniaux(2007)WangCox,LinWang(2006)WangSwissReBond4.3200411(EuropeanInvestmentBank,EIB)BNPParibasPartnerRe255.4()St×50001()[1(2002,64)]tjStmjj==−++∏(4.3.1)(2002,64)mtt++2002652002t+EIB/BNPBlakeBurrows(2001)EIB/BNP25EIB/BNPBlake,CairnsDowd(2006)EIB/BNPEIB/BNP1252EIB/BNP345()St(,)qxt1()[1(2002,64)]tjStqjj==−++∏1055.15.1.12003200069.6373.3319902.82.9(2005)Lee-CarterLee-CarterLee-Carter(Wilmoth,1993)5.1.2200611(20002003)CL(2000-2003)(19901993)76.73.180.93.179.74.883.74.7(,2006)(2006)(2007)2000CL(2000-2003)105.25.2.11%11DB5.2.2DC5.2.3200662620001999(,2004)(,2004)5.35.3.1(2006)(2006)Wang1200444%200410%(Walker,2006)223[2005]118(2000-2003)12(2000-2003)4,2006;,200620045.3.2121SwissRe23()()()45CowleyandCummins(2005)63CMIB4CMIB1990CMIB199951361234514AlhoJ.M.andSpencerB.,1985,UncertainpopulationForecasting,JournaloftheAmericanStatisticalAssociation80,306-314.BiffisE.,2005,Affineprocessesfordynamicmortalityandactuarialvaluations,Insurance:MathematicsandEconomics,37:443468.BlakeD.,2003,ReplytoSurvivorBonds:ACommentonBlakeandBurrows,TheJournalofRiskandInsurance,70(2):349-351.BlakeD.,CairnsA.andDowdK.,2006,LivingwithMortality:LongevityBondsandOtherMortality-linkedSecurities,BritishActuarialJournal,12(1):153-197.BlakeD.,CairnsA.,DowdK.andMacMinnR.,2006,LongevityBonds:FinancialEngineering,Valuation,andHedging,TheJournalofRiskandInsurance,73(4):647-672.BlakeD.andW.Burrows,2001,SurvivorBonds:HelpingtoHedgeMortalityRisk,TheJournalofRiskandInsurance,68(2):339-348.BrouhnsN.,DenuitM.andVermuntJ.K.,2002,APoissonlog-bilinearregressionapproachtotheconstructionofprojectedlifetablesInsurance:MathematicsandEconomics31373393.BrownJ.R.andOrszagP.R.,2006,ThepoliticalEconomyofGovernment