Résumé en anglais

In both arbitrage and utility pricing approaches, the fictitious completion appears as a very powerful tool that permits to generalize to an incomplete markets framework, results initially established in a complete markets setting. Does this technique permit to characterize the equilibrium pricing interval? In other words, does the set of prices that can be reached at the equilibrium for at least one distribution of preferences/endowments and for at least one completion coincide with the set of prices that can be reached at the equilibrium for at least one distribution of preferences/endowments? This note provides a negative answer.