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Finance and Stochastics

, Volume 11, Issue 1, pp 131–152 | Cite as

Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels

  • A. E. Kyprianou
  • B. A. Surya
Article

Abstract

We revisit the previous work of Leland [J Finance 49:1213–1252, 1994], Leland and Toft [J Finance 51:987–1019, 1996] and Hilberink and Rogers [Finance Stoch 6:237–263, 2002] on optimal capital structure and show that the issue of determining an optimal endogenous bankruptcy level can be dealt with analytically and numerically when the underlying source of randomness is replaced by that of a general spectrally negative Lévy process. By working with the latter class of processes we bring to light a new phenomenon, namely that, depending on the nature of the small jumps, the optimal bankruptcy level may be determined by a principle of continuous fit as opposed to the usual smooth fit. Moreover, we are able to prove the optimality of the bankruptcy level according to the appropriate choice of fit.

Keywords

Credit risk Endogenous bankruptcy Scale functions Fluctuation identity Continuous and smooth pasting principles Wiener–Hopf factorization 

JEL Classification

C61 

Mathematics Subject Classification (2000)

91B28 91B99 91B72 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesThe University of BathBathUK
  2. 2.Mathematical InstituteUniversity of UtrechtUtrechtThe Netherlands

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