Dividend barrier strategy: Proceed with caution

We consider a Lévy risk process and a Sparre-Andersen risk process with Parisian ruin in the presence of a constant dividend barrier. We demonstrate that with few exceptions, ruin occurs with probability one. Subsequently, generalizations to certain dependent risk processes are discussed. Despite the mathematical nature of this paper, its goal is to convey some simple conclusions to the actuarial community. The reader may focus solely on the introduction and conclusion sections (Sections 1 and 5, respectively) as well as the numerical illustrations.