Existence of collateral Equilibrium without survival assumption

this paper shows the existence of a collateral equilibrium without assuming any hypotheses on the strict positivity, be they individual initial endowments, including the ex post initial endowments, or aggregated initial endowments. because of dropping the strict positivity of social initial endowment we fail to get an equilibrium. instead, we get a quasi-equilibrium. then, appealing to the concept of irreducibility (introduced by mckenzie in 1959) which is adapted to the collateral model, we show that the quasi-equilibrium is indeed a legitime equilibrium.