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Optimal periodic dividend strategies for spectrally positive L\'evy risk processes with fixed transaction costs

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  • Benjamin Avanzi
  • Hayden Lau
  • Bernard Wong

Abstract

We consider the general class of spectrally positive L\'evy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot be paid at any time in real life, we study $\textit{periodic}$ dividend strategies whereby dividend decisions are made according to a separate arrival process. In this paper, we investigate the impact of fixed transaction costs on the optimal periodic dividend strategy, and show that a periodic $(b_u,b_l)$ strategy is optimal when decision times arrive according to an independent Poisson process. Such a strategy leads to lump sum dividends that bring the surplus back to $b_l$ as long as it is no less than $b_u$ at a dividend decision time. The expected present value of dividends (net of transaction costs) is provided explicitly with the help of scale functions. Results are illustrated.

Suggested Citation

  • Benjamin Avanzi & Hayden Lau & Bernard Wong, 2020. "Optimal periodic dividend strategies for spectrally positive L\'evy risk processes with fixed transaction costs," Papers 2003.13275, arXiv.org, revised May 2020.
    • Handle: RePEc:arx:papers:2003.13275
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    References listed on IDEAS

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    1. Loeffen, Ronnie L. & Renaud, Jean-François & Zhou, Xiaowen, 2014. "Occupation times of intervals until first passage times for spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1408-1435.
    2. Avanzi, Benjamin & Tu, Vincent & Wong, Bernard, 2016. "On The Interface Between Optimal Periodic And Continuous Dividend Strategies In The Presence Of Transaction Costs," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 709-746, September.
    3. Erhan Bayraktar & Masahiko Egami, 2008. "Optimizing venture capital investments in a jump diffusion model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 21-42, February.
    4. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    5. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2013. "On Optimal Dividends In The Dual Model," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 359-372, September.
    6. Zhao, Yongxia & Chen, Ping & Yang, Hailiang, 2017. "Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 135-146.
    7. Noba, Kei & Pérez, José-Luis & Yamazaki, Kazutoshi & Yano, Kouji, 2018. "On optimal periodic dividend strategies for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 29-44.
    8. Kei Noba & Jos'e-Luis P'erez & Kazutoshi Yamazaki & Kouji Yano, 2017. "On optimal periodic dividend strategies for L\'evy risk processes," Papers 1708.01678, arXiv.org, revised Feb 2018.
    9. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    10. Albrecher, Hansjörg & Cheung, Eric C.K. & Thonhauser, Stefan, 2011. "Randomized Observation Periods for the Compound Poisson Risk Model: Dividends," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 645-672, November.
    11. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2014. "Optimal dividends in the dual model under transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 133-143.
    12. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
    13. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2011. "Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs," European Journal of Operational Research, Elsevier, vol. 211(3), pages 568-576, June.
    14. Pérez, José-Luis & Yamazaki, Kazutoshi, 2017. "On the optimality of periodic barrier strategies for a spectrally positive Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 1-13.
    15. 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.
    16. José-Luis Pérez & Kazutoshi Yamazaki, 2018. "Mixed Periodic-Classical Barrier Strategies for Lévy Risk Processes," Risks, MDPI, vol. 6(2), pages 1-39, April.
    17. 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.
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    Cited by:

    1. Benjamin Avanzi & Hayden Lau & Bernard Wong, 2020. "Optimal periodic dividend strategies for spectrally negative L\'evy processes with fixed transaction costs," Papers 2004.01838, arXiv.org, revised Dec 2020.
    2. Benjamin Avanzi & Hayden Lau & Bernard Wong, 2020. "On the optimality of joint periodic and extraordinary dividend strategies," Papers 2006.00717, arXiv.org, revised Dec 2020.
    3. Wenyuan Wang & Xiang Yu & Xiaowen Zhou, 2021. "On optimality of barrier dividend control under endogenous regime switching with application to Chapter 11 bankruptcy," Papers 2108.01800, arXiv.org, revised Nov 2023.
    4. Avanzi, Benjamin & Lau, Hayden & Wong, Bernard, 2021. "On the optimality of joint periodic and extraordinary dividend strategies," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1189-1210.

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