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Two-side exit problems for taxed Lévy risk process involving the general draw-down time

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  • Wang, Wenyuan
  • Ming, Ruixing

Abstract

The literature has been witnessing an aroused interest in the study of the two-side exit problems for various models. Motivated by Kyprianou and Zhou (2009) and Li et al. (2018), the present paper concerns the two-side exit problems of the taxed spectrally negative Lévy risk process involving the general draw-down time. Our two-side exit problem is separated into two sub-problems: one being the Laplace transform of the up-exiting time of a certain level on the event that the taxed risk process up-crosses that level before the general draw-down time; the other being the Laplace transform of the draw-down time on the event that draw-down of the taxed risk process occurs before it up-crosses a certain level. Using a modified approximating method of Li et al. (2018) together with the excursion theory, solutions for the aforementioned two-side exit problems are obtained.

Suggested Citation

  • Wang, Wenyuan & Ming, Ruixing, 2018. "Two-side exit problems for taxed Lévy risk process involving the general draw-down time," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 66-74.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:66-74
    DOI: 10.1016/j.spl.2018.02.065
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    References listed on IDEAS

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    1. Wang, Wenyuan & Hu, Yijun, 2012. "Optimal loss-carry-forward taxation for the Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 121-130.
    2. Wang, Wenyuan & Ming, Ruixing & Hu, Yijun, 2011. "On the expected discounted penalty function for risk process with tax," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 489-501, April.
    3. Ming, Rui-Xing & Wang, Wen-Yuan & Xiao, Li-Qun, 2010. "On the time value of absolute ruin with tax," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 67-84, February.
    4. Avram, Florin & Vu, Nhat Linh & Zhou, Xiaowen, 2017. "On taxed spectrally negative Lévy processes with draw-down stopping," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 69-74.
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    Cited by:

    1. Wenyuan Wang & Zhimin Zhang, 2019. "Optimal loss-carry-forward taxation for L\'{e}vy risk processes stopped at general draw-down time," Papers 1904.08029, arXiv.org.

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