On the Existence of an Arrow-Radner Equilibrium in the Case of Complete Markets. A Remark

We consider a continuous time pure exchange stochastic economy with a financial sector. We 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. We 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.