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Potential Densities for Taxed Spectrally Negative Lévy Risk Processes

Author

Listed:
  • Wenyuan Wang

    (School of Mathematical Sciences, Xiamen University, Xiamen 361005, China)

  • Xiaowen Zhou

    (Department of Mathematics and Statistics, Concordia University, Montreal, QC H3G 1M8, Canada)

Abstract

This paper revisits the spectrally negative Lévy risk process embedded with the general tax structure introduced in Kyprianou and Zhou (2009). A joint Laplace transform is found concerning the first down-crossing time below level 0. The potential density is also obtained for the taxed Lévy risk process killed upon leaving [ 0 , b ] . The results are expressed using scale functions.

Suggested Citation

  • Wenyuan Wang & Xiaowen Zhou, 2019. "Potential Densities for Taxed Spectrally Negative Lévy Risk Processes," Risks, MDPI, vol. 7(3), pages 1-11, August.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:3:p:85-:d:254298
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    References listed on IDEAS

    as
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    3. Hao, Xuemiao & Tang, Qihe, 2009. "Asymptotic Ruin Probabilities of the Lévy Insurance Model under Periodic Taxation," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 479-494, November.
    4. Renaud, Jean-François, 2009. "The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 242-246, October.
    5. Eric C. K. Cheung & David Landriault, 2012. "On a Risk Model with Surplus-dependent Premium and Tax Rates," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 233-251, June.
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    7. 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.
    8. 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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