  Avanzi et al. (2016) recently studied an optimal dividend problem where
dividends are paid both periodically and continuously with different
transaction costs. In the Brownian model with Poissonian periodic dividend
payment opportunities, they showed that the optimal strategy is either of the
pure-continuous, pure-periodic, or hybrid-barrier type. In this paper, we
generalize the results of their previous study to the dual (spectrally positive
L\'evy) model. The optimal strategy is again of the hybrid-barrier type and can
be concisely expressed using the scale function. These results are confirmed
through a sequence of numerical experiments.
