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Martingale properties of self-enforcing debt

  • Bidian, Florin
  • Bejan, Camelia

Not-too-tight (NTT) debt limits are endogenous restrictions on debt that prevent agents from defaulting and opting for a specified continuation utility, while allowing for maximal credit expansion (Alvarez and Jermann, 2000). For an agent facing some fixed prices for the Arrow securities, we prove that discounted NTT debt limits must differ by a martingale. Discounted debt limits are submartingales/martingales under an interdiction to trade/borrow, and can be supermartingales under a temporary interdiction to trade. With high interest rates and borrowing limited by the agent's ability to repay debt out of his future endowments, nonpositive NTT debt limits are unique. With low interest rates, bubbles limited by the size of the total martingale components in debt limits can be sustained in equilibrium. Bubbles arise in response to debt limits more restrictive (at the prevailing interest rates) than the total amount of self-enforcing debt allowed by the underlying enforcement limitations.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36609.

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Date of creation: 01 Jan 2011
Date of revision: 12 Feb 2012
Handle: RePEc:pra:mprapa:36609
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  1. Alvarez, Fernando & Jermann, Urban J, 2001. "Quantitative Asset Pricing Implications of Endogenous Solvency Constraints," Review of Financial Studies, Society for Financial Studies, vol. 14(4), pages 1117-51.
  2. Gaetano Bloise & Pietro Reichlin, 2008. "Asset Prices, Debt Constraints and Inefficiency," EIEF Working Papers Series 0803, Einaudi Institute for Economics and Finance (EIEF), revised Mar 2008.
  3. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  4. Woodford, Michael, 1990. "Public Debt as Private Liquidity," American Economic Review, American Economic Association, vol. 80(2), pages 382-88, May.
  5. Gaetano Antinolfi & Costas Azariadis & James B. Bullard, 2007. "Monetary policy as equilibrium selection," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 331-342.
  6. 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.
  7. Kocherlakota, Narayana R, 1996. "Implications of Efficient Risk Sharing without Commitment," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 595-609, October.
  8. Azariadis, Costas & Kaas, Leo, 2013. "Endogenous credit limits with small default costs," Journal of Economic Theory, Elsevier, vol. 148(2), pages 806-824.
  9. Kevin X.D. Huang & Jan Werner, 2000. "Asset price bubbles in Arrow-Debreu and sequential equilibrium," Economic Theory, Springer, vol. 15(2), pages 253-278.
  10. Timothy J Kehoe & David K Levine, 1993. "Debt Constrained Asset Markets," Levine's Working Paper Archive 1276, David K. Levine.
  11. Bejan, Camelia & Bidian, Florin, 2010. "Limited enforcement, bubbles and trading in incomplete markets," MPRA Paper 36819, University Library of Munich, Germany, revised 20 Feb 2012.
  12. Kehoe, Timothy J & Levine, David K, 2001. "Liquidity Constrained Markets versus Debt Constrained Markets," Econometrica, Econometric Society, vol. 69(3), pages 575-98, May.
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