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On taxed spectrally negative Lévy processes with draw-down stopping

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  • Avram, Florin
  • Vu, Nhat Linh
  • Zhou, Xiaowen

Abstract

In this paper we consider a spectrally negative Lévy risk model with tax. With the ruin time replaced by a draw-down time with a linear draw-down function and for a constant tax rate, we find expressions for the present values of tax payments. They generalize previous results in Albrecher et al. (2008). Alternative proofs are given for the special case of Cramér–Lundberg risk models. Optimal barrier taxation policies are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:76:y:2017:i:c:p:69-74
    DOI: 10.1016/j.insmatheco.2017.06.005
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    References listed on IDEAS

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    3. 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.
    4. Hansjörg Albrecher & Florin Avram & Corina Constantinescu & Jevgenijs Ivanovs, 2014. "The Tax Identity For Markov Additive Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 245-258, March.
    5. Peter Carr, 2014. "First-order calculus and option pricing," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-19.
    6. 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.
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    8. Hansjoerg Albrecher & Jevgenijs Ivanovs, 2013. "Power identities for L\'evy risk models under taxation and capital injections," Papers 1310.3052, arXiv.org, revised Mar 2014.
    9. Albrecher, Hansjörg & Borst, Sem & Boxma, Onno & Resing, Jacques, 2009. "The tax identity in risk theory -- a simple proof and an extension," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 304-306, April.
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    Cited by:

    1. Budhi Surya & Wenyuan Wang & Xianghua Zhao & Xiaowen Zhou, 2020. "Parisian excursion with capital injection for draw-down reflected Levy insurance risk process," Papers 2005.09214, arXiv.org.
    2. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    3. Li, Shu & Zhou, Xiaowen, 2022. "The Parisian and ultimate drawdowns of Lévy insurance models," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 140-160.
    4. 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.
    5. Wenyuan Wang & Xueyuan Wu & Cheng Chi, 2019. "Optimal implementation delay of taxation with trade-off for L\'{e}vy risk Processes," Papers 1910.08158, arXiv.org.
    6. Wang, Wenyuan & Chen, Ping & Li, Shuanming, 2020. "Generalized expected discounted penalty function at general drawdown for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 12-25.
    7. 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.
    8. Wenyuan Wang & Xiaowen Zhou, 2019. "Potential Densities for Taxed Spectrally Negative Lévy Risk Processes," Risks, MDPI, vol. 7(3), pages 1-11, August.
    9. 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.
    10. Wenyuan Wang & Xiaowen Zhou, 2021. "A Drawdown Reflected Spectrally Negative Lévy Process," Journal of Theoretical Probability, Springer, vol. 34(1), pages 283-306, March.
    11. Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.

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    Keywords

    Lévy risk model with tax; Draw-down time;

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