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

Félix Locas and Jean-François Renaud

Insurance: Mathematics and Economics, 2025, vol. 120, issue C, 189-206

Abstract: We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative Lévy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the control problems considered by Kyprianou et al. (2012) and by Renaud (2019). Using the language of scale functions for Parisian fluctuation theory, and under the assumption that the density of the Lévy measure is completely monotone, we prove that a refraction dividend strategy is optimal and we characterize the optimal threshold. In particular, we study the effect of the rate of Parisian implementation delays on this optimal threshold.

Keywords: Dividend payments; Absolutely continuous strategies; Parisian ruin; Spectrally negative Lévy process; Refraction strategies (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:120:y:2025:i:c:p:189-206

DOI: 10.1016/j.insmatheco.2024.11.011

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