On the expected discounted penalty function for risk process driven by a spectrally negative Lévy process

The Expected Discounted Penalty Function (EDPF) was intro-duced in a series of now classical papers [Gerber and Shiu (1997), (1998a), (1998b) and Gerber and Landry (1998)]. Several authors have studied this function in more general settings [for instance Tsai and Willmot (2002), Li and Garrido (2005) and Garrido and Morales (2006)]. In Morales (2007) we find results for the EDPF in a perturbed risk process with a subordinator as the model for the aggregate claims and a Brownian motion as the model for the perturbation. In this note, we study the EDPF for a model where the aggregate claims are driven by a subordinator and the perturbation is modeled by a spec-trally negative Lévy process. This generalizes results found in Morales (2007)