Continuous time methods in finance A review and an assessment

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1、THEJOURNALOFFINANCE·VOL.LV,NO.4·AUGUST2000Continuous-TimeMethodsinFinance:AReviewandanAssessmentSURESHM.SUNDARESAN*ABSTRACTIsurveyandassessthedevelopmentofcontinuous-timemethodsinfinanceduringthelast30years.Thesubperiod1969to1980sawadizzyingpaceofdevelopmentwithseminalideasinderivativessecuritiesp

2、ricing,termstructuretheory,assetpricing,andoptimalconsumptionandportfoliochoices.Duringtheperiod1981to1999thetheoryhasbeenextendedandmodifiedtobetterexplainempiricalreg-ularitiesinvarioussubfieldsoffinance.Thislattersubperiodhasseensignificantprogressineconometrictheory,computationalandestimationm

3、ethodstotestandimplementcontinuous-timemodels.Capitalmarketfrictionsandbargainingis-suesarebeingincreasinglyincorporatedincontinuous-timetheory.THEROOTSOFMODERNCONTINUOUS-TIMEMETHODSinfinancecanbetracedbacktotheseminalcontributionsofMerton~1969,1971,1973b!inthelate1960sandearly1970s.Merton~1969!pi

4、oneeredtheuseofcontinuous-timemodelinginfinancialeconomicsbyformulatingtheintertemporalconsumptionandport-foliochoiceproblemofaninvestorinastochasticdynamicprogrammingset-ting.Merton~1973b!alsoshowedhowsuchaframeworkcanbeusedtodevelopequilibriumassetpricingimplications,therebysignificantlyextendin

5、gtheas-setpricingtheorytoricherdynamicsettingsandexpandingthescopeofap-plicationsofcontinuous-timemethodstostudyproblemsinfinancialeconomics.1Withinaspanofabout30yearsfromthepublicationofMerton'sinfluentialpapers,continuous-timemethodshavebecomeanintegralpartoffinancialeco-nomics.Indeed,incertainc

6、oreareasinfinance~suchas,e.g.,assetpricing,derivativesvaluation,termstructuretheory,andportfolioselection!continuous-timemethodshaveprovedtobethemostattractivewaytoconductresearchandgaineconomicintuition.Thecontinuous-timeapproachintheseareashasproducedmodelswitharichvarietyoftestableimplications.

7、Theeconometrictheoryfortestingcontinuous-timemodelshasmaderapidstridesinthelastdecadeandhasthuskeptpacewiththeimpressiveprogressonthetheoreticalfront.Onehopesthattheactualempiricalinvestigationsandestimationusing