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

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  • Renaud, Jean-François

Abstract

In this note, combining 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.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s016771522300202x
    DOI: 10.1016/j.spl.2023.109978
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    References listed on IDEAS

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    1. Jean-François Renaud, 2019. "De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes," Risks, MDPI, vol. 7(3), pages 1-11, July.
    2. Irmina Czarna & Zbigniew Palmowski, 2014. "Dividend Problem with Parisian Delay for a Spectrally Negative Lévy Risk Process," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 239-256, April.
    3. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    4. Loeffen, Ronnie L. & Renaud, Jean-François, 2010. "De Finetti's optimal dividends problem with an affine penalty function at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 98-108, February.
    5. Andreas E. Kyprianou & Víctor Rivero & Renming Song, 2010. "Convexity and Smoothness of Scale Functions and de Finetti’s Control Problem," Journal of Theoretical Probability, Springer, vol. 23(2), pages 547-564, June.
    6. 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.
    7. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    8. Luis Alvarez & Teppo Rakkolainen, 2009. "Optimal payout policy in presence of downside risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 27-58, March.
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