Optimal periodic dividend strategies for spectrally negative Lévy processes with fixed transaction costs

Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that are paid periodically real life, periodic dividend strategies were recently introduced (Albrecher et al. 2011). In this paper, we incorporate fixed transaction costs into model and study optimal strategy with for spectrally negative Lévy processes. The value function of a (bu,bl) calculated means exiting identities Itô's excusion when surplus process unbounded variation. We show sufficient condition optimality measure admits density which completely monotonic. Under such assumptions, confirmed to be optimal. Results illustrated.