Optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes: An alternative approach

The optimal dividend problem proposed in de Finetti 1] is to find the dividend-payment strategy that maximizes the expected discounted value of dividends which are paid to the shareholders until the company is ruined. Avram et al. 9] studied the case when the risk process is modelled by a general spectrally negative Lévy process and Loeffen 10] gave sufficient conditions under which the optimal strategy is of the barrier type. Recently Kyprianou et al. 11] strengthened the result of Loeffen 10] which established a larger class of Lévy processes for which the barrier strategy is optimal among all admissible ones. In this paper we use an analytical argument to re-investigate the optimality of barrier dividend strategies considered in the three recent papers.