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ID:7291755
大小:262.18 KB
页数:26页
时间:2018-02-10
《recursive macroeconomic theory self-insurance》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、Chapter17Self-Insurance17.1.IntroductionThischapterdescribesaversionofwhatissometimescalledasavingsproblem(e.g.,ChamberlainandWilson,2000).Aconsumerwantstomaximizetheexpecteddiscountedsumofaconcavefunctionofone-periodconsumptionrates,asinchapter8.However,theconsumeriscutofffromallinsurancemark
2、etsandalmostallassetmarkets.Theconsumercanpurchaseonlynonnegativeamountsofasinglerisk-freeasset.Theabsenceofinsuranceopportunitiesinducestheconsumertousevariationsovertimeinhisassetholdingstoacquire“self-insurance.”Thismodelisinterestingtouspartlyasabenchmarktocomparewiththecompletemarketsmod
3、elofchapter8andsomeoftherecursivecontractsmodelsofchapters20and21,whereinformationandenforcementproblemsrestrictallocationsrelativetochapter8,butneverthelesspermitmoreinsurancethanisallowedinthischapter.Aversionofthesingle-agentmodelofthischapterwillalsobeanimportantcomponentoftheincompletema
4、rketsmodelsofchapter18.Finally,thechapterprovidesourfirstencounterwiththepowerfulsupermartingaleconvergencetheorem.Tohighlighttheeffectsofuncertaintyandborrowingconstraints,weshallstudyversionsofthesavingsproblemunderalternativeassumptionsaboutthestringencyoftheborrowingconstraintandaboutwhethe
5、rthehousehold’sen-dowmentstreamisknownoruncertain.–699–700Self-Insurance17.2.Theconsumer’senvironmentAnagentordersconsumptionstreamsaccordingto∞Eβtu(c),(17.2.1)0tt=0whereβ∈(0,1),andu(c)isastrictlyincreasing,strictlyconcave,twicecon-tinuouslydifferentiablefunctionoftheconsumptionofasinglegoodc
6、.Theagentisendowedwithaninfiniterandomsequence{y}∞ofthegood.Eachtt=0period,theendowmenttakesoneofafinitenumberofvalues,indexedbys∈S.Inparticular,thesetofpossibleendowmentsisy17、Therearenoinsurancemarkets.Theagentcanholdnonnegativeamountsofasinglerisk-freeassetthathasanetrateofreturnr,where(1+r)β=1.Letat≥0betheagent’sassetsatthebeginningofperiodt,includingthecurrentrealizationoftheincomeprocess.(Laterweshalluseanalte
7、Therearenoinsurancemarkets.Theagentcanholdnonnegativeamountsofasinglerisk-freeassetthathasanetrateofreturnr,where(1+r)β=1.Letat≥0betheagent’sassetsatthebeginningofperiodt,includingthecurrentrealizationoftheincomeprocess.(Laterweshalluseanalte
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