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Martingale properties of self-enforcing debt

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  • Bidian, Florin
  • Bejan, Camelia

Abstract

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.

Suggested Citation

  • Bidian, Florin & Bejan, Camelia, 2011. "Martingale properties of self-enforcing debt," MPRA Paper 36609, University Library of Munich, Germany, revised 12 Feb 2012.
    • Handle: RePEc:pra:mprapa:36609
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Bidian, Florin, 2016. "Robust bubbles with mild penalties for default," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 141-153.
    2. Victor Filipe Martins da Rocha & Yiannis Vailakis, 2015. "Constrained Efficiency Without Commitment," Working Papers hal-01097121, HAL.
    3. Nicolas Houy & Frédéric Jouneau & François Le Grand, 2020. "Defaulting firms and systemic risks in financial networks: a normative approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 503-526, September.
    4. Bloise, Gaetano & Polemarchakis, Herakles & Vailakis, Yiannis, 2017. "Sovereign debt and incentives to default with uninsurable risks," Theoretical Economics, Econometric Society, vol. 12(3), September.
    5. Bejan, Camelia & Bidian, Florin, 2014. "Bubbles and trading in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 137-144.
    6. Victor Filipe Martins da Rocha & Toan Phan & Yiannis Vailakis, 2019. "Debt Limits and Credit Bubbles in General Equilibrium," Post-Print hal-02429759, HAL.
    7. Victor Filipe Martins da Rocha & Yiannis Vailakis, 2015. "On the Sovereign Debt Paradox," Working Papers hal-01097118, HAL.
    8. Neus Herranz & Stefan Krasa & Anne P. Villamil, 2015. "Entrepreneurs, Risk Aversion, and Dynamic Firms," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1133-1176.
    9. Bidian, Florin, 2015. "Portfolio constraints, differences in beliefs and bubbles," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 317-326.
    10. Bloise, Gaetano & Vailakis, Yiannis, 2024. "Sovereign debt crises and low interest rates," Journal of International Economics, Elsevier, vol. 150(C).
    11. Bidian, Florin & Bejan, Camelia, 2011. "Supplement to ``Martingale properties of self-enforcing debt''," MPRA Paper 36610, University Library of Munich, Germany, revised 12 Feb 2012.
    12. Gaetano Bloise & Pietro Reichlin & Mario Tirelli, 2013. "Fragility of Competitive Equilibrium with Risk of Default," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(2), pages 271-295, April.
    13. 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.
    14. Victor Filipe Martins da Rocha & Yiannis Vailakis, 2014. "Self-enforcing Debt, Reputation, and the Role of Interest Rates," Working Papers hal-01097114, HAL.
    15. Florin Bidian & Camelia Bejan, 2015. "Martingale properties of self-enforcing debt," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 35-57, September.
    16. Filipe Martins da Rocha & Yiannis Vailakis, 2017. "Borrowing in Excess of Natural Ability to Repay," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 42-59, January.
    17. Jan Werner, 2012. "Rational Asset Pricing Bubbles Revisited," 2012 Meeting Papers 1165, Society for Economic Dynamics.
    18. V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2017. "On the sovereign debt paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(4), pages 825-846, December.
    19. Werner, Jan, 2014. "Rational asset pricing bubbles and debt constraints," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 145-152.

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    More about this item

    Keywords

    rational bubbles; endogenous debt limits; not-too-tight constraints; self-enforcing debt; limited enforcement;
    All these keywords.

    JEL classification:

    • E0 - Macroeconomics and Monetary Economics - - General
    • G0 - Financial Economics - - General

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