Before revision: In this paper, we complement the existing literature on the occupation time in the red (below level 0) of a spectrally negative L\'evy process, and later extend the analysis to the refracted spectrally negative L\'evy process. For both classes of processes, we derive an explicit expression for the distribution of such occupation timeup to an independent exponential time. As an application, we consider theinverse occupation time (also known as the time of cumulative Parisian ruin in \mbox{%DIFAUXCMD guerinrenaud20150pt%DIFAUXCMD ), where ruin is deemed to occur at the earliest time the risk process cumulatively stays below a critical level over a pre-determined time-threshold.
After revision: In this paper, we complement the existing literature on the occupation time in the red (below level 0) of a spectrally negative L\'evy process, and later extend the analysis to the refracted spectrally negative inverse occupation time (also known as the time of cumulative Parisian ruin in \mbox{%DIFAUXCMD guerinrenaud20150pt%DIFAUXCMD ), where ruin is deemed to occur at the earliest time the risk process cumulatively stays below a critical level over a pre-determined time-threshold.