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The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure

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  • Renaud, Jean-François

Abstract

We study the distribution of tax payments in the model of Kyprianou and Zhou [Kyprianou, A.E., Zhou, X., 2009. General tax structures and the Lévy insurance risk model. J. Appl. Probab. (in press)], that is a Lévy insurance risk model with a surplus-dependent tax rate. More precisely, after a short discussion on the so-called tax identity, we derive a recursive formula for arbitrary moments of the discounted tax payments until ruin and we identify the distribution of the tax payments when there is no force of interest.

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  • 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.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:242-246
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    References listed on IDEAS

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    1. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
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    Cited by:

    1. Wenyuan Wang & Xiaowen Zhou, 2019. "Potential Densities for Taxed Spectrally Negative Lévy Risk Processes," Risks, MDPI, vol. 7(3), pages 1-11, August.
    2. Griffin, Philip S., 2020. "General tax structures for a Lévy insurance risk process under the Cramér condition," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1368-1387.
    3. Dalal Al Ghanim & Ronnie Loeffen & Alex Watson, 2018. "The equivalence of two tax processes," Papers 1811.01664, arXiv.org, revised Oct 2019.
    4. 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.
    5. 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.
    6. 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.
    7. Cui, Zhenyu & Nguyen, Duy, 2016. "Omega diffusion risk model with surplus-dependent tax and capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 150-161.
    8. 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.
    9. Zhenyu Cui, 2014. "Omega risk model with tax," Papers 1403.7680, arXiv.org.
    10. Al Ghanim, Dalal & Loeffen, Ronnie & Watson, Alexander R., 2020. "The equivalence of two tax processes," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 1-6.

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