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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.

Path functionals of a class of Lévy insurance risk processes