  In the setting of a L\'evy insurance risk process, we present some results
regarding the Parisian ruin problem which concerns the occurrence of an
excursion below zero of duration bigger than a given threshold $r$. First, we
give the joint Laplace transform of ruin-time and ruin-position (possibly
killed at the first-passage time above a fixed level $b$), which generalises
known results concerning Parisian ruin. This identity can be used to compute
the expected discounted penalty function via Laplace inversion. Second, we
obtain the $q$-potential measure of the process killed at Parisian ruin. The
results have semi-explicit expressions in terms of the $q$-scale function and
the distribution of the L\'evy process.
