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

Bidian, Florin and Bejan, Camelia (2011): Supplement to Martingale properties of self-enforcing debt''.

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## 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.

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