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General Draw-Down Times for Refracted Spectrally Negative Lévy Processes

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  • Xuan Huang

    (Hunan Normal University)

  • Jieming Zhou

    (Hunan Normal University
    Hunan Normal University, College of Hunan Province)

Abstract

In this paper, we prove several results involving a general draw-down time from the running maximum for refracted spectrally negative Lévy processes. Using an approximation method, which is excursion theory at its heart, we find expressions for the Laplace transforms for the two-sided exit problems which are related to the draw-down time and an expression for the associated potential measure. The results are expressed in terms of scale functions.

Suggested Citation

  • Xuan Huang & Jieming Zhou, 2022. "General Draw-Down Times for Refracted Spectrally Negative Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 875-891, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-022-09933-6
    DOI: 10.1007/s11009-022-09933-6
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    References listed on IDEAS

    as
    1. Yingchun Deng & Xuan Huang & Ya Huang & Xuyan Xiang & Jieming Zhou, 2020. "n-Dimensional Laplace Transforms of Occupation Times for Pre-Exit Diffusion Processes," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 345-360, March.
    2. Lkabous, Mohamed Amine & Czarna, Irmina & Renaud, Jean-François, 2017. "Parisian ruin for a refracted Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 153-163.
    3. Zhao, Xianghua & Dong, Hua & Dai, Hongshuai, 2018. "On spectrally positive Lévy risk processes with Parisian implementation delays in dividend payments," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 176-184.
    4. Wenyuan Wang & Xiaowen Zhou, 2021. "A Drawdown Reflected Spectrally Negative Lévy Process," Journal of Theoretical Probability, Springer, vol. 34(1), pages 283-306, March.
    5. Landriault, David & Renaud, Jean-François & Zhou, Xiaowen, 2011. "Occupation times of spectrally negative Lévy processes with applications," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2629-2641, November.
    6. 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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