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
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8.εsatis estheno-unbounded-arbitragecondition(Page[41]).εsatis esboundedarbitrage(CPP)(Allouch[2,4]).Thesetofrationalallocations,A,iscompact.εsatis esinconsequentialarbitrage(Pageetal.[48]).Thesetofrationalutilitypossibilities,U,iscompact.εhasanequilibrium.
[A.7]uiiscontinuous.
[A.8]uiisuniformlynon-satiated,andsatis esoneofthefollowingtwomutuallyexclusiveconditions:(a)thenormalizedgradienttoanyclosedsetofindi erentvectorsde neaclosedsetor(b)noindi erencesurfacecontainshalflines.
Theorem5.2Letεbeaneconomysatisfyingassumption[A.1],[A,2],[A,7]and
[A,8].Thenthefollowingstatementsareequivalent:
1.Theeconomyεhaslimitedarbitrage.
2.U(ε)iscompact.
3.P(ε)iscompact.
Corollary5.2Letεbeaneconomysatisfyingassumption[A.1],[A,2],[A’.3],
[A,4],[A.5],[A’.6],[A,7]and[A,8].Thenthefollowingstatementsareequivalent:
1.εsatis estheno-arbitragepricesystemcondition(Werner[55]).
2.εsatis estheweak-no-arbitragecondition(Hart[27]).
3.εsatis estheno-unbounded-arbitragecondition(Page[41]).
4.Thesetofrationalallocations,A,iscompact.
5.εsatis esinconsequentialarbitrage(Pageetal.[48]).
6.εsatis esboundedarbitrage(CPP)(Allouch[2,4]).
7.Thesetofrationalutilitypossibilities,U,iscompact.
8.εhasanequilibrium.
9.Theeconomyεhaslimitedarbitrage.
10.P(ε)iscompact.
References
[1]Allingham,M.,Arbitrage,St.martin’sPress,NewYork1991.
[2]Allouch,N.,Equilibriumandnomarketarbitrage,WorkingPaper.CERMSEM,
UniversitedeParisI,1999.
[3]AlouchN.,LeVan,C.,andPage,F.H.Jr,Arbitrage,equilibrium,andnonsa-
tiation,tyoescript,UniversityParis1,CERMSEM,2002.
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