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

Thai Ha-Huy (1) , Cuong Le Van (2, 3, 4, 5)

1 EPEE - Centre d'Etudes des Politiques Economiques
2 IPAG Business School
3 CES - Centre d'économie de la Sorbonne
4 PSE - Paris School of Economics
5 TIMAS - Institute of Mathematics and Applied Science

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.

Mots clés: Asset market equilibrium; Beliefs strong equivalence; Individually rational attainable allocations; Individually rational utility set; No-arbitrage condition; No-arbitrage prices

Domaines: 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⟩