Journal article: We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a financial structure with possibly long-term assets. We address the question of the continuity of the set of marketable payoffs with respect to the asset prices. In a previous paper, we have exhibited a sufficient condition,which is based only on the returns of the assets.However, it is never satisfied in the structures with re-trading [See Bonnisseau and Chéry (Ann Finance 10:523–552, 2014)], which is a very common feature in many papers following the model of Magill and Quinzii (Theory of Incomplete Markets, MIT Press, Cambridge, 1996). The main purpose of this paper is to address this issue. We exhibit a new sufficient condition for general financial structures, which enjoys the property to be inherited by the re-trading extension of a financial structure. So, we pave the way for equilibrium existence results under assumptions only on the fundamentals of the economy.