Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes

  • F. Hubalek
  • E. Kyprianou
Conference paper
Part of the Progress in Probability book series (PRPR, volume 63)


We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Lévy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new family of scale functions belonging to the Gaussian Tempered Stable Convolution (GTSC) class. We give particular emphasis to special cases as well as cross-referencing their analytical behaviour against known general considerations.


Scale functions spectrally negative Lévy processes Mittag-Leffler functions Wiener-Hopf factorization 


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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Financial and Actuarial MathematicsVienna University of TechnologyViennaAustria
  2. 2.Department of Mathematical SciencesThe University of BathBathUK

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