Special, conjugate and complete scale functions for spectrally negative Lévy processes

Abstract

Following recent developments in Hubalek and Kyprianou [28] the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative Lévy processes which are completely explicit. This will follow as a consequence of an observation in the aforementioned paper which permits feeding the theory of Bernstein functions directly into the Wiener-Hopf factorization for spectrally negative Lévy processes. Many new, concrete examples of scale functions are offered although the methodology in principle delivers still more explicit examples than those listed here. © 2008 Applied Probability Trust.