Stockastic Dominance----Wiki

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1、StochasticdominanceFromWikipedia,thefreeencyclopedia[1][2]Stochasticdominanceisaformofstochasticordering.Thetermisusedindecisiontheoryanddecisionanalysistorefertosituationswhereonegamble(aprobabilitydistributionoverpossibleoutcomes,alsoknownasprospects)ca

2、nberankedassuperiortoanothergamble.Itisbasedonpreferencesregardingoutcomes.Apreferencemightbeasimplerankingofoutcomesfromfavoritetoleastfavored,oritmightalsoemployavaluemeasure(i.e.,anumberassociatedwitheachoutcomethatallowscomparisonofmultiplesofoneoutco

3、mewithanother,suchastwoinstancesofwinningadollarvs.oneinstanceofwinningtwodollars.)Onlylimitedknowledgeofpreferencesisrequiredfordeterminingdominance.Riskaversionisafactoronlyinsecondorderstochasticdominance.Stochasticdominancedoesnotgiveacompleteordering

4、:Forsomepairsofgambles,neitheronestochasticallydominatestheother,yettheycannotbesaidtobeequal.Arelatedconceptnotincludedunderstochasticdominanceisdeterministicdominance,whichoccurswhentheleastpreferableoutcomeofgambleAismorevaluablethanthemosthighlyprefer

5、redoutcomeofgambleB.Contents•1Statewisedominance•2First-orderstochasticdominance•3Second-orderstochasticdominanceo3.1Second-orderstochasticdominanceinportfolioanalysiso3.2Sufficientconditionsforsecond-orderstochasticdominanceo3.3Necessaryconditionsforseco

6、nd-orderstochasticdominance•4Third-orderstochasticdominanceo4.1Sufficientconditionforthird-orderstochasticdominanceo4.2Necessaryconditionsforthird-orderstochasticdominance•5Higher-orderstochasticdominance•6Stochasticdominanceconstraints•7ReferencesStatewi

7、sedominanceThesimplestcaseofstochasticdominanceisstatewisedominance(alsoknownasstate-by-statedominance),definedasfollows:gambleAisstatewisedominantovergambleBifAgivesabetteroutcomethanBineverypossiblefuturestate(moreprecisely,atleastasgoodanoutcomeinevery

8、state,withstrictinequalityinatleastonestate).Forexample,ifadollarisaddedtooneormoreprizesinalottery,thenewlotterystatewisedominatestheoldone.Similarly,ifariskinsurancepolicyhasalowerpremiumandabettercoveragethananot