We consider the optimal dividend problem under a habit formation constraint that prevents the dividend rate to fall below a certain proportion of its historical maximum, the so-called drawdown constraint. This is an extension of the optimal Duesenberry's ratcheting consumption problem, studied...

We revisit the dividend payment problem in the dual model of Avanzi et al. Using the fluctuation theory of spectrally positive Levy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Levy processes. Moreover, we characterize the optimal...

We analyze the optimal dividend payment problem in the dual model under constant transaction costs. We show, for a general spectrally positive Levy process, an optimal strategy is given by a (c1, c2)-policy that brings the surplus process down to c1 whenever it reaches or exceeds c2 for some...