A note on the optimal dividends problem with transaction costs in a spectrally negative Lévy model with Parisian ruin

In this note, merging ideas from Loeffen (2009) and Renaud (2019), we prove that an (a,b)-strategy maximizes dividend payments subject to fixed transaction costs in a spectrally negative Lévy model with Parisian ruin, as long as the tail of the Lévy measure is log-convex.