Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities

We consider a model with an inffnite number of states of nature, von Neumann - Morgenstern utilities, where agents have different probabil- ity beliefs and where short sells are allowed. We show that no-arbitrage conditions, deffned for ffnite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an inffnite num- ber of states of nature. However, 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.