Occupation times of refracted Levy processes with jumps having rational Laplace transforms

We investigate a refracted Levy process driven by a jump diffusion process, whose jumps have rational Laplace transforms. For such a stochastic process, formulas for the Laplace transform of its occupation times are deduced. To derive the main results, some modifications on our previous approach have been made. In addition, we obtain a very interesting identity, which is conjectured to hold for a general refracted Levy process.