分野別セミナー

講演要旨：
　　We study the scale function for the class of spectrally
negative Lévy　processes with phase-type jumps.
We consider both the compound Poisson case and the unbounded
　variation case with diffusion components, and obtain the
corresponding scale functions explicitly. Motivated by the fact
that the class of phase-type distributions is dense in the class
of all positive-valued distributions, we propose a new approach
to approximating the scale function for a general spectrally
negative Lévy process. We illustrate, in numerical examples, its
effectiveness by obtaining the scale functions for Lévy processes
with long-tail distributed jumps.