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Optimal Default Boundary in Discrete Time Models

by Agata Altieri of the Universitá di Padova, and
Tiziano Vargiolu of the Universitá di Padova

June 2002

Abstract: In this paper we solve the problem of determining the default time of a firm in such a way as to maximize its total value, which includes bankruptcy costs and tax benefits, with the condition that the value of equity must be nonnegative. By applying dynamic programming in discrete time, we find results which extends those of Merton (1974), and we give an application for the approximation of models driven by a Brownian motion or a Poisson process.

JEL Classification: C61, G13, G32, G33.

AMS Classification: 60G40, 62L15, 91B70.

Keywords: Credit and default risk, optimal stopping, dynamic programming.

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