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.
CITATION STYLE
Hubalek, F., & Kyprianou, E. (2011). Old and New Examples of Scale Functions for Spectrally Negative Lévy Processes. In Progress in Probability (Vol. 63, pp. 119–145). Birkhauser. https://doi.org/10.1007/978-3-0348-0021-1_8
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