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1、ClassicalSubjectiveExpectedUtility∗∗∗†SimoneCerreiaVioglio,FabioMaccheroni,MassimoMarinacci,andLuigiMontrucchio∗UniversitaBocconi,Milano,Italy,and`†UniversitadiTorino,Torino,Italy`SubmittedtoProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmericaWeconsi
2、derdecisionmakerswhoknowthatpayoffrelevantobelicitpriorprobabilitiesonthemthroughhypothetical(sincemodelsservationsaregeneratedbyaprocessthatbelongstoagivenarenotingeneralobservable)bettingbehavior.Nevertheless,ourba-classM,aspostulatedinWald(1950).Weincorporatethi
3、ssicrepresentationresult,Proposition1,showsthat,underSavage’sWaldeanpieceofobjectiveinformationwithinanotherwisesubaxiomsP.1-P.6andtheaboveconsistencycondition,actsarerankedjectivesettingalaSavage(1954)andshowthatthisleadstoaaccordingtothecriteriontwostagesubjectiv
4、eexpectedutilitymodelthataccountsforboth∫(∫)stateandmodeluncertainty.V(f)=u(f(s))dm(s)d(m)[1]∆Sexpectedutility
5、modeluncertainty
6、stateuncertaintywhereisasubjectivepriorprobabilityonmodels,whosesupportisincludedinM.WecallthisrepresentationClassicalSubjectiveAbbrevi
7、ations:DM,decisionmaker;SEU,subjectiveexpectedutilityExpectedUtilitybecauseoftheclassicalWaldeantenetonwhichitrelies.onsideradecisionmakerwhoisevaluatingactswhoseoutcomesThepriorisasubjectiveprobabilitythatmayalsoreflectsomeCdependonsomeverifiablestates,thatis,onobs
8、ervations(work-personalinformationonmodelsthattheDMmayhave,inadditioners’outputs,urns’drawings,ratesofinflation,andthelike).IfthetotheobjectiveinformationM.UniquenessofcorrespondstotheDMbelievesthatobservationsaregeneratedbysomeprobabilitylinearindependenceoftheset
9、M.Forexample,Mislinearlyin-model,twosourcesofuncertaintyaffecthisevaluation:modelun-dependentwhenitsmembersarepairwiseorthogonal.Remarkably,certaintyandstateuncertainty.Theformerisabouttheprobabilitysomeimportanttimeseriesmodelswidelyusedineconomicandfi-modelthatgen
10、eratesobservations,thelatterisaboutthestatethatnancialapplicationssatisfythiscondition,asdiscussedlaterintheobtains(andthatdeterminesacts’outcome
