On existence of an Arrow-Radner equilibrium in the case of complete markets. A remark

The authors consider a continuous time pure exchange stochastic economy with a financial sector. They first give a proof of the ‘equivalence’ of Arrow-Radner and Arrow-Debreu equilibria under the assumption that the gains associated to the securities form a local martingale generator. The authors then give a simple proof of existence of an Arrow-Debreu equilibrium in the separable utility case, under the assumption that either all agents have finite marginal utility at zero or aggregate endowment is uniformly bounded below.