Existence of equilibrium on asset markets with a countably infinite number of states

Thai Ha-Huy and Cuong Le Van ()
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Cuong Le Van: IPAG Business School, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, TIMAS - Institute of Mathematics and Applied Science

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We consider a model with a countably infinite number of states of nature. The agents have equivalent probability beliefs and von Neumann–Morgenstern utilities. The No-Arbitrage Prices in this paper are, up to a scalar, the marginal utilities. We introduce the Beliefs Strong Equivalence and the No Half Line Condition of the same type conditions. Under these conditions, the No Arbitrage price condition is sufficient for the existence of an equilibrium when the commodity space is lp,1≤p<+∞. This No Arbitrage condition is necessary and sufficient for the existence of equilibrium when the total endowment is in l∞. Moreover, it is equivalent to the compactness of the individually rational utility set.

Keywords: Asset market equilibrium; Beliefs strong equivalence; Individually rational attainable allocations; Individually rational utility set; No-arbitrage condition; No-arbitrage prices (search for similar items in EconPapers)
Date: 2017-12
Note: View the original document on HAL open archive server: https://hal.science/hal-02877952v1
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Published in Journal of Mathematical Economics, 2017, 73, pp.44-53. ⟨10.1016/j.jmateco.2017.07.001⟩

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Related works:
Working Paper: Existence of equilibrium on asset markets with a countably infinite number of states (2023)
Journal Article: Existence of equilibrium on asset markets with a countably infinite number of states (2017)
Working Paper: Existence of equilibrium on asset markets with a countably infinite number of states (2017)
Working Paper: Existence of equilibrium on asset markets with a countably infinite number of states (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-02877952

DOI: 10.1016/j.jmateco.2017.07.001

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