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