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

•A model with an infinite number of states of nature, von Neumann–Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed.•Propose a no-arbitrage condition in the infinite dimension economies.•Discuss about these conditions.

We consider a model with an infinite number of states of nature, von Neumann–Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed. 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. However, if the individually rational utility set UU is compact, we obtain an equilibrium. We give conditions which imply the compactness of UU. We give examples of non-existence of equilibrium when these conditions do not hold.