We consider an infinite-horizon exchange economy with incomplete markets and collateral constraints.As in the two-period model of Geanakoplos and Zame (2002), households can default on their liabilities at any time, and financial securities are only traded if the promises associated with these securities are backed by collateral.We examine an economy with a single perishable consumption good, where the only collateral available consists of productive assets.In this model, competitive equilibria always exist and we show that, under the assumption that all exogenous variables follow a Markov chain, there also exist stationary equilibria.These equilibria can be characterized by a mapping from the exogenous shock and the current distribution of financial wealth to prices and portfolio choices.We develop an algorithm to approximate this mapping numerically and discuss ways to implement the algorithm in practice.A computational example demonstrates the performance of the algorithm and shows some quantitative features of equilibria in a model with collateral and default.

Trading volume of infinitely lived securities, such as equity, is generically zero in Lucas asset pricing models with heterogeneous agents. More generally, the end‐of‐period portfolio of all securities is constant over time and states in the generic economy. General equilibrium restrictions rule out trading of equity after an initial period. This result contrasts the prediction of portfolio allocation analyses that portfolio rebalancing motives produce nontrivial trade volume. Therefore, other causes of trade must be present in asset markets with large trading volume.