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Strategic Default Jump as Impulse Control in Continuous Time

by Hisashi Nakamura of the University of Tokyo

February 18, 2008

Abstract: This paper presents a new approach for modeling an optimal debt contract in continuous time. It examines a competing contract design in a continuous-time environment with Markov income shocks and costly verifiable information. It shows that an optimal contract has the form of a long-term debt contract that permits a debtor's strategic default and debt restructuring. The default is characterized by a recurrent, optimal impulse control beyond default. Numerical examples show that the equilibrium probability of the default is decreasing in the monitoring technology level when the default causes a big wealth loss.

JEL Classification: C73, D82, G33.

Keywords: Default, Costly verification, Continuous time, Competing contract design, Impulse control.

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