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Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral

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  • Felix Kubler
  • Karl Schmedders

Abstract

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. Copyright The Econometric Society 2003.
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Suggested Citation

  • Felix Kubler & Karl Schmedders, 2001. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Discussion Papers 1319, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1319
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    References listed on IDEAS

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    6. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2000. "Default in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 1247, Cowles Foundation for Research in Economics, Yale University.
    7. Aloisio Araujo & Mário Rui Páscoa & Juan Pablo Torres-Martínez, 2002. "Collateral Avoids Ponzi Schemes in Incomplete Markets," Econometrica, Econometric Society, vol. 70(4), pages 1613-1638, July.
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