Making promises in infinite-horizon economies with default and collateral

We study an infinite-horizon economy with incomplete markets where default is explicitly allowed, contrary to the GE1 model (where default is ruled out by assumption). The time and uncertainty are modeled by a countable infinite event-tree with a unique initial node at initial date, and with a continuum of branches at each node of the tree. If we allow agents to sell promises subject to the purchase of durable goods serving as collateral, then it is possible to prove the existence of equilibria without imposing either constraint on agent's asset holdings, or assumption on ex post endowments. The proof is independent of the manner in which households discount the future.