On the refracted–reflected spectrally negative Lévy processes

On the refracted–reflected spectrally negative Lévy processes

We study a combination of the refracted and reflected Lévy processes. Given a spectrally negative Lévy 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....

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Bibliographic Details
Published in:Stochastic processes and their applications Vol. 128; no. 1; pp. 306 - 331
Main Authors: Pérez, José-Luis, Yamazaki, Kazutoshi
Format: Journal Article
Language:English
Published: Elsevier B.V 01-01-2018
Subjects:
Fluctuation theory
Insurance risk
Lévy processes
Scale functions
90B22
Scale functions
60G51
Fluctuation theory
Insurance risk
91B30
Lévy processes
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Summary:We study a combination of the refracted and reflected Lévy processes. Given a spectrally negative Lévy 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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2017.03.024