On Optimal Dividends in the Dual Model

Abstract

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 barrier using the functional inverse of a scale function. We also consider the capital injection problem and show that its value function has a very similar form to the one in which the horizon is the time of ruin.

Keywords: Dual model, dividends, capital injections, spectrally positive Levy processes, scale functions

JEL Classification: C44, C61, G24, G32, G35