Abstract: This article surveys some recent progress on arbitrage and equilibrium in asset exchange economies. Using the basic geometry of arbitrage, the relationships between various no-arbitrage conditions appeared in the literature are presented. The rel
AMO-AdvancedModellingandOptimization,Volume5,Number3,2003
ArbitrageandEquilibriuminAssetExchange
Economies:ASurvey1
HongbinDong,GuangyaChenandShouyangWang2
InstituteofSystemsScience,AcademyofMathematicsandSystemsSciences,
ChineseAcademyofSciences,Beijing100080,China
Abstract:Thisarticlesurveyssomerecentprogressonarbitrageand
http://www.77cn.com.cningthebasicgeometryof
arbitrage,therelationshipsbetweenvariousno-arbitrageconditionsap-
pearedintheliteraturearepresented.Therelationshipsbetweensome
ofthebasicno-arbitrageconditionstogetherwiththeexistenceresultof
anequilibriuminDanaetal.[16]provideanoverviewofsu cientcon-
ditionsforequilibrium.Undercertainconditionsthevariousno-arbitrage
conditionsintheliteratureareequivalentandnecessaryandsu cient
fortheexistenceofanequilibrium.
Keywords:Arbitrage;Equilibrium;Compactness;Cones;Uniformity
1Introduction
SincethepioneeringcontributionsofGrandmont[21,22,23],Green[25],andHart
[27],therelationshipbetweenarbitrageandequilibriuminassetexchangeeconomiesallowingshortsaleshasbeenoneofthehotsubjectineconomicand nancialstud-ies.Anarbitrageopportunityisamutuallycompatiblesetofnettradeswhichareutilitynondecreasingand,atmost,costlesstomake.Conditionsthatlimitutil-ityarbitragearecentraltoestablishingexistenceingeneralequilibriummodelsofexchangeeconomieswithunboundedshortsales(see,forexample,Page[40]andWerner[55]).Whenunboundedshortsalesareallowed,asisnaturalinassetmar-ketmodels,agents’choicersetsareboundedfrombelow,andasaconsequence,unboundedandmutuallycompatiblearbitrageopportunitiescanbeexhaustedmayfailtoexist,andthus,equilibriummayfailtoexist.Byassumingthatmarketsadmit“noarbitrage”,theeconomycanbeboundedendogenously butthisisnot1
2SupportedbyNSFC,CASandMADIS.Thecorrespondingauthor,Email:sywang@http://www.77cn.com.cn
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