Path functionals of a class of Lévy insurance risk processes

Abstract

Abstract. We study expected discounted penalty functionals for a class of Lévy processes having a component given by the difference of two independent Poisson compound processes, and a perturbation term given by an α-stable process. We obtain a formula for the Laplace transforms of the expected discounted penalty functionals, as well as explicit representations of such functionals as infinite series of convolutions of given functions. We illustrate our results in some particular examples.

The distribution and asympotic behaviour of the negative Wiener–Hopf factor for Lévy processes with rational positive jumps

“…Using the second equality in Lemma 5.2 in Kolkovska and Martín-González [2016], it follows that lim u→∞ χ q,S (u)…”

“…We also need the following two lemmas. The first one is a well-known formula in interpolation theory, while the second one is part of the proof of [7,Proposition 5.4].…”