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.
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.
Titre
en
Existence of equilibrium on asset markets with a countably infinite number of states
Auteur(s)
Thai Ha-Huy1
, Cuong Le Van2, 3, 4, 5
1
EPEE -
Centre d'Etudes des Politiques Economiques
( 19169 )
- 4, boulevard François Mitterrand, 91025 EVRY CEDEX
- France
Université d'Évry-Val-d'Essonne EA 2177 ( 300306 )
2
IPAG Business School
( 542840 )
- 184 boulevard Saint-Germain, 75006 Paris
- France
3
CES -
Centre d'économie de la Sorbonne
( 15080 )
- Maison des Sciences Économiques - 106-112 Boulevard de l'Hôpital - 75647 Paris Cedex 13
- France
Université Paris 1 Panthéon-Sorbonne UMR8174 ( 7550 )
;
Centre National de la Recherche Scientifique UMR8174 ( 441569 )
4
PSE -
Paris School of Economics
( 301309 )
- 48 boulevard Jourdan 75014 Paris
- France
Université Paris 1 Panthéon-Sorbonne ( 7550 )
;
École normale supérieure - Paris ( 59704 )
;
Université Paris Sciences et Lettres ( 564132 )
;
École des hautes études en sciences sociales ( 99539 )
;
École des Ponts ParisTech ( 301545 )
;
Centre National de la Recherche Scientifique ( 441569 )
;
Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement ( 577435 )
5
TIMAS -
Institute of Mathematics and Applied Science
( 557622 )
- Viêt Nam
Page/Identifiant
44-53
Langue du document
Anglais
Volume
73
Nom de la revue
Journal of Mathematical Economics
(ISSN : 0304-4068)
Publié par Elsevier
Revue non référencée dans Sherpa-Romeo
Vulgarisation
Non
Comité de lecture
Oui
Audience
Internationale
Date de publication
2017-12
Date de publication électronique
2017-07-20
Domaine(s)
Sciences de l'Homme et Société/Economies et finances
Thai Ha-Huy, Cuong Le Van. Existence of equilibrium on asset markets with a countably infinite number of states. Journal of Mathematical Economics, 2017, 73, pp.44-53. ⟨10.1016/j.jmateco.2017.07.001⟩. ⟨hal-02877952⟩