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Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities

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  • Jos'e-Luis P'erez
  • Kazutoshi Yamazaki

Abstract

Avanzi et al. (2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities, they showed that the optimal strategy is either of the pure-continuous, pure-periodic, or hybrid-barrier type. In this paper, we generalize the results of their previous study to the dual (spectrally positive L\'evy) model. The optimal strategy is again of the hybrid-barrier type and can be concisely expressed using the scale function. These results are confirmed through a sequence of numerical experiments.

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  • Jos'e-Luis P'erez & Kazutoshi Yamazaki, 2016. "Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities," Papers 1612.02444, arXiv.org, revised Jan 2018.
    • Handle: RePEc:arx:papers:1612.02444
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    References listed on IDEAS

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    1. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
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    11. Benjamin Avanzi & Jos'e-Luis P'erez & Bernard Wong & Kazutoshi Yamazaki, 2016. "On optimal joint reflective and refractive dividend strategies in spectrally positive L\'evy models," Papers 1607.01902, arXiv.org, revised Nov 2016.
    12. Yongwu Li & Zhongfei Li & Yan Zeng, 2016. "Equilibrium Dividend Strategy with Non-exponential Discounting in a Dual Model," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 699-722, February.
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    16. 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.
    17. Yongxia Zhao & Rongming Wang & Dingjun Yao & Ping Chen, 2015. "Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 272-295, October.
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    Cited by:

    1. 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.
    2. José-Luis Pérez & Kazutoshi Yamazaki, 2018. "Mixed Periodic-Classical Barrier Strategies for Lévy Risk Processes," Risks, MDPI, vol. 6(2), pages 1-39, April.
    3. 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.
    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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