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# Supplement to Martingale properties of self-enforcing debt''

## Author

Listed:
• Bidian, Florin
• Bejan, Camelia

## Abstract

We present some complementary results to Bidian and Bejan (2012). Part 1 provides necessary and sufficient transversality conditions for an agent's optimization problem. They are extensions to stochastic environments of the conditions given by Kocherlakota (1992), or alternatively, extensions to nonzero debt constraints of the corresponding conditions in Forno2003}. Part \ref{ap:B} presents an elementary proof of the characterization of NTT debt limits (Theorem 3.5 in the main paper) for the case when debt constraints bind in bounded time, that requires no martingale techniques or boundedness assumptions on the discounted debt limits. Part \ref{ap:C} complements results in Section 5.1 (in the main paper), showing that all the equilibria that can sustain bubbles under an interdiction to trade can be achieved from fixed, zero initial wealth for the agents. Thus endogeneity of debt limits causes multiplicity of not only asset prices (through bubbles), but also of real equilibrium allocations.

## Suggested Citation

• 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.
• Handle: RePEc:pra:mprapa:36610
as

File URL: https://mpra.ub.uni-muenchen.de/36610/1/MPRA_paper_36610.pdf
File Function: original version

## References listed on IDEAS

as
1. Kocherlakota, Narayana R., 1992. "Bubbles and constraints on debt accumulation," Journal of Economic Theory, Elsevier, vol. 57(1), pages 245-256.
2. 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.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. 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.
2. Bejan, Camelia & Bidian, Florin, 2014. "Bubbles and trading in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 137-144.
3. Werner, Jan, 2014. "Rational asset pricing bubbles and debt constraints," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 145-152.

### Keywords

rational bubbles; transversality conditions; endogenous debt limits; not-too-tight constraints; self-enforcing debt; limited enforcement;

### JEL classification:

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

### NEP fields

This paper has been announced in the following NEP Reports:

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