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Collateral, default penalties and almost finite-time solvency

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  • Martins-da-Rocha, Victor Filipe
  • Vailakis, Yiannis

Abstract

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.

Suggested Citation

  • Martins-da-Rocha, Victor Filipe & Vailakis, Yiannis, 2008. "Collateral, default penalties and almost finite-time solvency," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 670, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:epgewp:670
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    References listed on IDEAS

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    1. 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.
    2. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2005. "Default and Punishment in General Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 1-37, January.
    3. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-880, July.
    4. A. Araujo & M. R. Páscoa & P. K. Monteiro, 1997. "Incomplete markets, continuum of states and default," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 205-213.
    5. 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 1142-1164, December.
    6. David K. Levine & William R. Zame, 2002. "Does Market Incompleteness Matter?," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.
    7. Aloisio Araujo & Mário Rui Páscoa & Juan Pablo Torres-Martínez, 2002. "Collateral Avoids Ponzi Schemes in Incomplete Markets," Econometrica, Econometric Society, pages 1613-1638.
    8. Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
    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 & Alvaro Sandroni, 1999. "On the Convergence to Homogeneous Expectations when Markets Are Complete," Econometrica, Econometric Society, vol. 67(3), pages 663-672, May.
    11. Felix Kubler & Karl Schmedders, 2003. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Econometrica, Econometric Society, vol. 71(6), pages 1767-1793, November.
    12. 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.
    13. Timothy J. Kehoe & David K. Levine, 1993. "Debt-Constrained Asset Markets," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 865-888.
    14. 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.
    15. 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.
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    Cited by:

    1. Rubén Poblete-Cazenave & Juan Torres-Martínez, 2013. "Equilibrium with limited-recourse collateralized loans," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(1), pages 181-211, May.

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