Before revision:  Recent results have shown, in the dual (spectrally positive  ) model,  the optimality of a periodic barrier strategy where dividends are paid at dividend-decision times  if and only if the surplus is above some level.
After revision:  Recent results have shown, in the dual (spectrally positive ) model, the optimality of a periodic barrier strategy , which pays dividends at Poissonian dividend-decision times if and only if the surplus is above some level.