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

TL;DR

This paper derives formulas for the Laplace transform of occupation times of a refracted Levy process with jumps having rational Laplace transforms, and proposes a conjecture for a general identity in such processes.

Contribution

It introduces new formulas for occupation times of refracted Levy processes with rational Laplace transform jumps and presents a conjecture for a broader class of these processes.

Findings

Formulas for Laplace transforms of occupation times derived

An interesting identity conjectured for general refracted Levy processes

Modifications made to previous methods for main results

Abstract

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.