managing demographic risk in enhanced pensions

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1、ManagingdemographicriskinenhancedpensionsSusannaLevantesiandMassimilianoMenziettiAbstract.ThispaperdealswithdemographicriskanalysisinEnhancedPensions,i.e.,long-termcare(LTC)insurancecoverfortheretired.Bothdisabilityandlongevityrisksaffectsuchcover.Specifically,weconcentrateontheriskofsystematic

2、deviationsbetweenprojectedandrealisedmortalityanddisability,adoptingamultiplescenarioapproach.Tothispurposewestudythebehaviouroftherandomriskreserve.Moreover,weanalysetheeffectofdemographicriskonrisk-basedcapitalrequirements,explaininghowtheycanbereducedthrougheithersafetyloadingorcapitalalloc

3、ationstrategies.Aprofitanalysisisalsoconsidered.Keywords:longtermcarecovers,enhancedpension,demographicrisks,riskreserve,sol-vencyrequirements1IntroductionThe“EnhancedPension”(EP)isalong-termcare(LTC)insurancecoverfortheretired.ItoffersanimmediatelifeannuitythatisincreasedoncetheinsuredbecomesL

4、TCdisabledandrequiresasinglepremium.EPisaffectedbydemographicrisks(longevityanddisabilityrisks)arisingfromtheuncertaintyinfuturemortalityanddisabilitytrendsthatcausetheriskofsystematicdeviationsfromtheexpectedvalues.SomeanalysesoftheseargumentshavebeenperformedbyFerriandOlivieri[1]andOlivieria

5、ndPitacco[6].Toevaluatesuchariskwecarryoutananalysistakingintoaccountamultiplescenarioapproach.Todefineasetofprojectedscenariosweconsidergeneralpopulationstatisticsofmortalityanddisability.Wefirstlyanalysethebehaviouroftheriskreserve,thenwedefinethecapitalrequirementsnecessarytoguaranteethesolven

6、cyoftheinsurer.Finallywestudytheportfolioprofitability.Suchananalysiscannotbecarriedoutbyanalyticaltools,butrequiresaMonteCarlosimulationmodel.Thepaperisorganisedasfollows.InSection2wedefinetheactuarialframeworkforEPs.InSection3wedevelopninedemographicscenariosanddescribethroughasuitablemodelhow

7、theycanchangeovertime.InSection4wepresentarisktheorymodelbasedontheportfolioriskreserveandtheRiskBasedCapitalrequirementsnecessarytopreservetheinsurancecompanyfromfailureswithafixedconfidenceM.Corazzaetal.(eds.),MathematicalandStatistical