We consider a model with an infinite numbers of states of nature, von Neumann - Morgenstern utilities and where agents have different prob- ability beliefs. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. How- ever, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold.
Thai Ha-Huy, Cuong Le Van, and Manh-Hung Nguyen, “Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities”, Mathematical Social Sciences, vol. 79, January 2016, pp. 30–39.