On the Refracted-Reflected Spectrally Negative Lévy Processes

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.

28 pages, forthcoming in Stochastic Processes and their Applications

References in corpus (2)

• On the optimal dividend problem for a spectrally negative Lévy process
• On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes

Cited by in corpus (3)

• On optimal joint reflective and refractive dividend strategies in spectrally positive Lévy models
• Spectrally negative Lévy processes with Parisian reflection below and classical reflection above
• Phase-type Approximation of the Gerber-Shiu Function