Optimal Periodic Dividend Strategies for Spectrally Positive Lévy Risk Processes With Fixed Transaction Costs

Abstract

We consider the general class of spectrally positive Levy 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 strategies whereby dividend decisions are made according to a Poisson arrival process. In this paper, we investigate the impact of fixed transaction costs on the optimal periodic dividend strategy, and show that a periodic (b u , b l ) strategy is optimal. Such a strategy leads to lump sum dividends that bring the surplus back to b l as long as it is no less than b u at a dividend decision time. The expected present value of dividends (net of transaction costs) is provided explicitly with the help of scale functions. Results are illustrated.