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

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  • Locas, Félix
  • Renaud, Jean-François

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.

Suggested Citation

  • Locas, Félix & Renaud, Jean-François, 2025. "Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 189-206.
    • Handle: RePEc:eee:insuma:v:120:y:2025:i:c:p:189-206
    DOI: 10.1016/j.insmatheco.2024.11.011
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    References listed on IDEAS

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    1. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
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    7. Renaud, Jean-François, 2024. "A note on the optimal dividends problem with transaction costs in a spectrally negative Lévy model with Parisian ruin," Statistics & Probability Letters, Elsevier, vol. 206(C).
    8. Mohamed Amine Lkabous & Jean-François Renaud, 2019. "A unified approach to ruin probabilities with delays for spectrally negative Lévy processes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(8), pages 711-728, September.
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