On the Refracted-Reflected Spectrally Negative Levy Processes
Stochastic Processes and their Applications, 128(1), 306-331, 2018.
28 Pages Posted: 6 Jun 2019
Date Written: May 10, 2017
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
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