On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency

► A dual risk model with a dividend barrier strategy is studied. ► We propose that dividend decisions are made periodically whereas solvency is monitored continuously. ► The Laplace transform of the time to ruin and the expected present value of dividends until ruin are derived. ► Our analysis relies not only on integro-differential equations but also on probabilistic arguments. ► Numerical illustrations are given to compare our model with the classical barrier strategy.