We consider the general class of spectrally positive Lévy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends are paid periodically in real life, we study periodic dividend...

In the classical optimal dividends problem, dividend decisions are allowed to be made at any point in time - according to a continuous strategy. Depending on the surplus process that is considered and whether dividend payouts are bounded or not, optimal strategies are generally of a band,...