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Martingale properties of self-enforcing debt

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

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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. 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. Asset price bubbles limited by the size of the total martingale components in debt limits can be sustained in equilibrium. They can counteract the effects of a credit tightening in the economy.

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