Stationary equlibria in asset-pricing models with incomplete markets and collateral

We consider an infinite-horizon exchange economy with incomplete markets and collateral constraints. As in the two-period model of Geanakoplos and Zame (1998) households can default on their liabilities at any time without any utility penalties or loss of reputation. Financial securities are therefore 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. These equilibria can be characterized by a mapping from the exogenous shock and the current distribution of financial wealth to prices and portofolio choices. We develop an algorithm in practice. Two computational examples demonstrate the performance of the algorithm and show some quantitative features of equilibria in models with collateral and default.