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 in¢nitely lived securities, such as equity, is generically zero in Lucas asset pricing models with heterogeneous agents. More generally, the endof-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. EACH DAY FINDS INVESTORS actively trading assets. However, the Lucas (1978) asset pricing model, the foundation of much of general equilibrium ¢nance theory, says little about volume since it assumes a representative agent (or, equivalently, several identical investors) and has no trade in equilibrium. If markets are complete or can be completed through dynamic trading of the available securities (as in Kreps (1982)), then asset prices evolve as if there is a single agent even when there are several agents with di¡erent tastes and income processes. Therefore, representative agent models are generally valuable for a theory of asset pricing with complete markets. This approach says nothing about trading volume, which is unfortunate since data on volume may give us additional information about the operation of asset markets and the underlying tastes of investors. This paper examines equilibrium asset trading in the Lucas model with agent heterogeneity and dynamically complete markets. We characterize equilibrium in a constructive fashion and present an algorithm to compute equilibrium prices and trading volume.We ¢nd that trading volume of in¢nitely lived assets is zero in the generic economy. In general, we ¢nd each investor's portfolio is constant over time and states once one controls for the maturing of ¢nitely lived assets.The intuition is clear and follows directly from linear algebra and market completeness. Suppose, for the sake of simplicity, that the current dividend summarizes all information about future dividends. 1 Then the dividend process is a

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This paper shows that the latest generation of asset pricing models with long‐run risk exhibit economically significant nonlinearities, and thus the ubiquitous Campbell‐Shiller log‐linearization can generate large numerical errors. These errors translate in turn to considerable errors in the model predictions, for example, for the magnitude of the equity premium or return predictability. We demonstrate that these nonlinearities arise from the presence of multiple highly persistent processes, which cause the exogenous states to attain values far away from their long‐run means with nonnegligible probability. These extreme values have a significant impact on asset price dynamics.

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