  Path decomposition is performed to analyze the pre-supremum, post-supremum,
post-infimum and the intermediate processes of a spectrally negative Levy
process taken up to an independent exponential time T as motivated by the aim
of finding the joint distribution of the maximum loss and maximum gain. In
addition, the joint distribution of the supremum and the infimum before an
exponential time is displayed. As an application of path decomposition, the
distributions of supremum of the post-infimum process and the maximum loss of
the post-supremum process are obtained.
