Generalized refracted Lévy process and its application to exit problem

Abstract

Generalizing Kyprianou--Loeffen's refracted Lévy processes, we define a new refracted Lévy process which is a Markov process whose positive and negative motions are Lévy processes different from each other. To construct it we utilize the excursion theory. We study its exit problem and the potential measures of the killed processes. We also discuss approximation problem.

33 pages

References in corpus (2)

• Spectrally negative Lévy processes with Parisian reflection below and classical reflection above
• Lévy insurance risk processes with parisian type severity of debt