On the refracted–reflected spectrally negative Lévy processes

José-Luis Pérez and Kazutoshi Yamazaki

Stochastic Processes and their Applications, 2018, vol. 128, issue 1, 306-331

Abstract: 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.

Keywords: Lévy processes; Fluctuation theory; Scale functions; Insurance risk (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2017.03.024

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