Discounted Penalty Function at Parisian Ruin for Lévy Insurance Risk Process
arXiv:1706.01962
Abstract
In the setting of a Lévy 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 . First, we give the joint Laplace transform of ruin-time and ruin-position (possibly killed at the first-passage time above a fixed level ), 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 -potential measure of the process killed at Parisian ruin. The results have semi-explicit expressions in terms of the -scale function and the distribution of the Lévy process.