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On Scale Functions of Spectrally Negative Lévy Processes with Phase-type Jumps (江上雅彦氏との共著)

Hold Date
2010-06-04 15:50〜2010-06-04 17:20
Ito Campus, Faculty of Mathematics building, seminar room 3
Object person
Kazutoshi YAMAZAKI (Osaka University)

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.