On optimal periodic dividend strategies in the dual model with diffusion

In this paper, we consider a periodic dividend strategy with exponential inter-dividend-decision times and continuous monitoring of solvency. Assuming hyperexponential gains, we show that a periodic barrier dividend strategy is the periodic strategy that maximizes the expected present value of dividends paid until ruin. Interestingly, a 'liquidation-at-first-opportunity' strategy is optimal in some cases where the surplus process has a positive drift. Results are illustrated.