In this note we give semi-explicit solutions for r-balayages of matrix-exponential Lévy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by Mordecki in , Asmussen, Avram and Pistorius in , Chen, Lee and Sheu in , and many others.
- First exit
- Lévy process
- Matrix-exponential distribution
- Ruin theory