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Dividend barrier strategy: Proceed with caution

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  • Sendova, Kristina P.
  • Yang, Chen
  • Zhang, Ruixi

Abstract

We consider a Lévy risk process and a Sparre-Andersen risk process with Parisian ruin in the presence of a constant dividend barrier. We demonstrate that with few exceptions, ruin occurs with probability one. Subsequently, generalizations to certain dependent risk processes are discussed. Despite the mathematical nature of this paper, its goal is to convey some simple conclusions to the actuarial community. The reader may focus solely on the introduction and conclusion sections (Sections 1 and 5, respectively) as well as the numerical illustrations.

Suggested Citation

  • Sendova, Kristina P. & Yang, Chen & Zhang, Ruixi, 2018. "Dividend barrier strategy: Proceed with caution," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 157-164.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:157-164
    DOI: 10.1016/j.spl.2018.01.016
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    References listed on IDEAS

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    1. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
    2. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
    3. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 691-701, December.
    4. Ronnie Loeffen & Irmina Czarna & Zbigniew Palmowski, 2011. "Parisian ruin probability for spectrally negative L\'{e}vy processes," Papers 1102.4055, arXiv.org, revised Mar 2013.
    5. Dassios, Angelos & Wu, Shanle, 2008. "Parisian ruin with exponential claims," LSE Research Online Documents on Economics 32033, London School of Economics and Political Science, LSE Library.
    6. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. Yang, Chen & Sendova, Kristina P. & Li, Zhong, 2020. "Parisian ruin with a threshold dividend strategy under the dual Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 135-150.
    2. A. S. Dibu & M. J. Jacob, 2022. "On a double barrier hybrid dividend strategy in a compound Poisson risk model with stochastic income," Annals of Operations Research, Springer, vol. 315(2), pages 969-984, August.
    3. Ganjar Alfian & Muhammad Syafrudin & Norma Latif Fitriyani & Sahirul Alam & Dinar Nugroho Pratomo & Lukman Subekti & Muhammad Qois Huzyan Octava & Ninis Dyah Yulianingsih & Fransiskus Tatas Dwi Atmaji, 2023. "Utilizing Random Forest with iForest-Based Outlier Detection and SMOTE to Detect Movement and Direction of RFID Tags," Future Internet, MDPI, vol. 15(3), pages 1-16, March.
    4. Liu, Zhang & Chen, Ping & Hu, Yijun, 2020. "On the dual risk model with diffusion under a mixed dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 376(C).

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