On the Refracted-Reflected Spectrally Negative Levy Processes

Stochastic Processes and their Applications, 128(1), 306-331, 2018.

28 Pages Posted: 6 Jun 2019

See all articles by José-Luis Pérez

José-Luis Pérez

Centro de Investigacion en Matematicas (CIMAT) - Department of Probability and Statistics

Kazutoshi Yamazaki

Kansai University - Department of Mathematics

Date Written: May 10, 2017

Abstract

We study a combination of the refracted and reflected Levy processes. Given a spectrally negative Levy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a constant rate is subtracted from the increments of the process. Using the scale functions, we compute the resolvent measure, the Laplace transform of the occupation times as well as other fluctuation identities that will be useful in applied probability including insurance, queues, and inventory management.

Keywords: Levy processes, fluctuation theory, scale functions, insurance risk

JEL Classification: C44, C61, G24, G32, G35

Suggested Citation

Pérez, José-Luis and Yamazaki, Kazutoshi, On the Refracted-Reflected Spectrally Negative Levy Processes (May 10, 2017). Stochastic Processes and their Applications, 128(1), 306-331, 2018.. Available at SSRN: https://ssrn.com/abstract=3390016

José-Luis Pérez

Centro de Investigacion en Matematicas (CIMAT) - Department of Probability and Statistics ( email )

Guanajuato
Mexico

Kazutoshi Yamazaki (Contact Author)

Kansai University - Department of Mathematics ( email )

3-3-35 Yamate-cho, Suita-shi
Osaka, 564-8680
Japan

HOME PAGE: http://https://sites.google.com/site/kyamazak/

Register to save articles to
your library

Register

Paper statistics

Downloads
4
Abstract Views
38
PlumX Metrics