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We consider de Finetti's optimal dividends problem with absolutely continuousstrategies in a spectrally negative L\'evy model with Parisian ruin as thetermination time. The problem considered is essentially a generalization ofboth the control problems considered by Kyprianou, Loeffen & P\'erez (2012) andby Renaud (2019). Using the language of scale functions for Parisianfluctuation theory, and under the assumption that the density of the L\'evymeasure is completely monotone, we prove that a refraction dividend strategy isoptimal and we characterize the optimal threshold. In particular, we study theeffect of the rate of Parisian implementation delays on this optimal threshold.

Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin