*Article* **Potential Densities for Taxed Spectrally Negative Lévy Risk Processes**

**Wenyuan Wang 1 and Xiaowen Zhou 2,\***


Received: 29 May 2019; Accepted: 17 July 2019; Published: 2 August 2019

**Abstract:** This paper revisits the spectrally negative Lévy risk process embedded with the general tax structure introduced in Kyprianou and Zhou (2009). A joint Laplace transform is found concerning the first down-crossing time below level 0. The potential density is also obtained for the taxed Lévy risk process killed upon leaving [0, *b*]. The results are expressed using scale functions.

**Keywords:** spectrally negative Lévy process; general tax structure; first crossing time; joint Laplace transform; potential measure
