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Collateral, default penalties and almost finite-time solvency

  • Felipe Martins-da-Rocha
  • Yiannis Vailakis

We argue that it is possible to adapt the approach of imposing restrictions on available plans through finitely effective debt constraints, introduced by Levine and Zame (1996), to encompass models with default and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002) and Páscoa and Seghir (2008) the concept of almost finite-time solvency. We show that the conditions imposed in these two papers to rule out Ponzi schemes implicitly restrict actions to be almost finite-time solvent. We define the notion of equilibrium with almost finite-time solvency and look on sufficient conditions for its existence. Assuming a mild assumption on default penalties, namely that agents are myopic with respect to default penalties, we prove that existence is guaranteed (and Ponzi schemes are ruled out) when actions are restricted to be almost finite-time solvent. The proof is very simple and intuitive. In particular, the main existence results in Araujo et al. (2002) and Páscoa and Seghir (2008) are simple corollaries of our existence result.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 122247000000002049.

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Date of creation: 04 Apr 2008
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Handle: RePEc:cla:levarc:122247000000002049
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1988. "Default and Efficiency in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 879R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1989.
  2. 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.
  3. Timothy J. Kehoe & David K. Levine, 1992. "Debt constrained asset markets," Working Papers 445, Federal Reserve Bank of Minneapolis.
  4. David K. Levine & William R. Zame, 1992. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," UCLA Economics Working Papers 666, UCLA Department of Economics.
  5. Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," DELTA Working Papers 92-26, DELTA (Ecole normale supérieure).
  6. Araujo, A. & Monteiro, P. K. & Páscoa, M.R., . "Incomplete markets, continuum of states and default," CORE Discussion Papers RP 1297, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Zame, William R, 1993. "Efficiency and the Role of Default When Security Markets Are Incomplete," American Economic Review, American Economic Association, vol. 83(5), pages 1142-64, December.
  8. David K. Levine & William R. Zame, 2002. "Does Market Incompleteness Matter?," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.
  9. Aloisio Araujo & Paulo K. Monteiro & M´rio Rui P´ascoa, 1996. "Infinite Horizon Incomplete Markets With A Continuum Of States," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 119-132.
  10. 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.
  11. P. Dubey & J. Geanakoplos & M . Shubik, 2001. "Default and Punishment in General Equilibrium," Department of Economics Working Papers 01-07, Stony Brook University, Department of Economics.
  12. Hernandez D., Alejandro & Santos, Manuel S., 1996. "Competitive Equilibria for Infinite-Horizon Economies with Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 102-130, October.
  13. Dubey, Pradeep & Shubik, Martin, 1979. "Bankruptcy and optimality in a closed trading mass economy modelled as a non-cooperative game," Journal of Mathematical Economics, Elsevier, vol. 6(2), pages 115-134, July.
  14. Aloisio Araujo & Alvaro Sandroni, 1999. "On the Convergence to Homogeneous Expectations when Markets Are Complete," Econometrica, Econometric Society, vol. 67(3), pages 663-672, May.
  15. Fernando Alvarez & Urban J. Jermann, 2000. "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica, Econometric Society, vol. 68(4), pages 775-798, July.
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