Abstract
In this paper, adopting the Poisson approach and the perturbation approach for spectrally negative Lévy processes (often abbreviated as SNLP), we consider some joint Laplace transforms of the last exit time from two semi-infinite interval, the value of the process, and the associated occupation time. Motivated by Li and Cai (2018), Li et al. (2017), Our results can recover some previous results when taking the limit to infinity in our results.
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