Abstract
In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative Lévy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized scale functions. For step weight functions, the Laplace transforms can be further expressed in terms of scale functions.
Acknowledgments
We thank anonymous referees for very helpful suggestions. Yun Hua and Bo Li thank Concordia University where the first draft of this paper was completed during their visits in early 2017. Xiaowen Zhou thanks National Center for Theoretical Sciences (NCTS) where this paper was revised during his visit.
Disclosure statement
No potential conflict of interest was reported by the author(s).