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Optimal dividend-payout in random discrete time

Author

Listed:
  • Albrecher Hansjörg
  • Bäuerle Nicole

    (University of Karlsruhe (TH), Institute für Stochastics, Karlsruhe, Deutschland)

  • Thonhauser Stefan

    (University of Lausanne, Faculty of Business and Economics, Lausanne)

Abstract

Assume that the surplus process of an insurance company is described by a general Lévy process and that possible dividend pay-outs to shareholders are restricted to random discrete times which are determined by an independent renewal process. Under this setting we show that the optimal dividend pay-out policy is a band-policy. If the renewal process is a Poisson process, it is further shown that for Cramér–Lundberg risk processes with exponential claim sizes and its diffusion limit the optimal policy collapses to a barrier-policy. Finally, a numerical example is given for which the optimal bands can be calculated explicitly. The random observation procedure studied in this paper also allows for an interpretation in terms of a random walk model with a certain type of random discounting.

Suggested Citation

  • Albrecher Hansjörg & Bäuerle Nicole & Thonhauser Stefan, 2011. "Optimal dividend-payout in random discrete time," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 251-276, September.
    • Handle: RePEc:bpj:strimo:v:28:y:2011:i:3:p:251-276:n:2
    DOI: 10.1524/stnd.2011.1097
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    References listed on IDEAS

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    1. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    2. 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.
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    Cited by:

    1. Gordienko, E. & Vázquez-Ortega, P., 2018. "Continuity inequalities for multidimensional renewal risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 48-54.
    2. Chen, Xu & Xiao, Ting & Yang, Xiang-qun, 2014. "A Markov-modulated jump-diffusion risk model with randomized observation periods and threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 76-83.
    3. Avanzi, Benjamin & Tu, Vincent & Wong, Bernard, 2014. "On optimal periodic dividend strategies in the dual model with diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 210-224.

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