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Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels. (English) Zbl 1143.91020
The authors assume that the value of underlying assets of a firm is modelled using a general exponential spectrally negative Lévy process. It is shown that an analytical treatment of the optimal bankruptcy level is possible and that the smooth-pasting condition is not always appropriate. The analytical proof is given for the fact that, depending on the path regularity of the underlying Lévy process, a principle of either smooth pasting or continuous pasting should be applied, accordingly to unbounded or bounded variation of Lévy process, respectively. Some notions of fluctuation theory of Lévy processes, including a number of identities expressed in terms of scale functions, from which it is possible to give analytic expressions for the value and debt of a firm, are discussed. The computation of the optimal endogenous bankruptcy level is also discussed.

##### MSC:
 91G40 Credit risk 91B99 Mathematical economics 91B72 Spatial models in economics 60G51 Processes with independent increments; Lévy processes
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##### References:
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