Arbitrage and Equilibrium in Asset Exchange Economies A Surv(5)

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

Inconsequentialarbitrageandboundedarbitrageworkdi erently.Theyimplythecompactnessofthesetofutilitypossibilitieswithoutanytypeofuniformity,andtherefore,issu cientfortheexistencewithoutuniformity againviatheDanaetal.[16]result.

Usingthegeometryofarbitrage,Allouchetal.[5]sharpenandextendtheresultofPageetal.[48]showingtheequivalenceoftheconditionsofHart[27]andWerner

[55].Allouchetal.[5]establishthisequivalencewithoutanyassumptionsconcern-inguniformityornonsatiation.InPageetal.[48],theequivalenceofHartandWernerisobtainedassumingaveryweakformofnonsatiation(duetoWerner[55])andastrongformofuniformity(i.e.uniformityofarbitrageopportunities).Inaddi-tion,Allouchetal.[3]showunderweakuniformityonlythattheconditionsofHartandWernerimplytheconditionofinconsequentialarbitrage,introducedinPageetal.[48].Pageetal.[48]showthisaswell,butrequireWernernonsatiationandstronguniformity.Iftheeconomysatis esuniformityofarbitrageopportunities,lo-calnonsatiationatrationalallocationandweakno-half-lines,thentheHart-Wernerno-arbitrageconditionsandinconsequentialarbitrageareequivalent,andarenec-essaryandsu cientforthecompactnessofthesetofutilitypossibilitiesandtheexistenceofanequilibrium.Ifwestrengthentheweakno-half-linesconditiontoWerner’sconditionofno-half-lines,thentheHart-Wernerno-arbitrageconditionsandinconsequentialarbitrageareequivalenttono-unbounded-arbitrage,andallarenecessaryandsu cientforthecompactnessofthesetofrationalallocations,thecompactnessofthesetofutilitypossibilities,andtheexistenceofanequilibrium.Thepaperisorganizedasfollows.Basicmodelofanunboundedexchangeecon-omyandsomede nitionsarepresentedinSection2.Section3isdedicatedtopresenttherelationshipbetweenthevariousno-arbitrageconditionsfoundintheliteratureandthestrengthoftheboundednessimpliedbytheseconditions.InSection4,Suf- cientconditionsfortheexistenceofanequilibriumisaddressed.Finally,Section5showsthatundercertainconditions,thevariousno-arbitrageconditionsappearedintheliteratureareequivalentandnecessaryandsu cientfortheexistenceofanequilibrium.

2Themodel

Weconsideraneconomyε=(Xi,ui,ei)mi=1withmagentsandlgoods.Agenti hasconsumptionsetXi Rl,utilityfunctionui(.),andendowmentei,Agentispreferredsetatxi∈Xiis

Pi(xi)={x∈Xi|ui(x)>ui(xi)},

whiletheweakpreferredsetatxi∈Xiis

i(xi)={x∈Xi|ui(x)≥ui(xi)}.P

179

百度搜索“77cn”或“免费范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，免费范文网，提供经典小说教育文库Arbitrage and Equilibrium in Asset Exchange Economies A Surv(5)在线全文阅读。