  We revisit the dividend payment problem in the dual model of Avanzi et al.
([2], [1], and [3]). Using the fluctuation theory of spectrally positive
L\'{e}vy processes, we give a short exposition in which we show the optimality
of barrier strategies for all such L\'{e}vy processes. Moreover, we
characterize the optimal barrier using the functional inverse of a scale
function. We also consider the capital injection problem of [3] and show that
its value function has a very similar form to the one in which the horizon is
the time of ruin.
