IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1910.08158.html
   My bibliography  Save this paper

Optimal implementation delay of taxation with trade-off for L\'{e}vy risk Processes

Author

Listed:
  • Wenyuan Wang
  • Xueyuan Wu
  • Cheng Chi

Abstract

In this paper we consider two problems on optimal implementation delay of taxation with trade-off for spectrally negative L\'{e}vy insurance risk processes. In the first case, we assume that an insurance company starts to pay tax when its surplus reaches a certain level $b$ and at the termination time of the business there is a terminal value incurred to the company. The total expected discounted value of tax payments plus the terminal value is maximized to obtain the optimal implementation level $b^*$. In the second case, the company still pays tax subject to an implementation level $a$ but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the capital injection costs is maximized to obtain the optimal implementation level $a^*$. Numerical examples are also given to illustrate the main results in this paper.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1910.08158
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1910.08158
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    4. Wenyuan Wang & Ping Chen & Shuanming Li, 2019. "Generalized Expected Discounted Penalty Function at General Drawdown for L\'{e}vy Risk Processes," Papers 1906.01449, arXiv.org.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Wei, Li, 2009. "Ruin probability in the presence of interest earnings and tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 133-138, August.
    10. 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.
    11. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    12. 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.
    13. Albrecher, Hansjörg & Badescu, Andrei & Landriault, David, 2008. "On the dual risk model with tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1086-1094, June.
    14. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. 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.
    3. 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.
    4. Wenyuan Wang & Xiaowen Zhou, 2019. "Potential Densities for Taxed Spectrally Negative Lévy Risk Processes," Risks, MDPI, vol. 7(3), pages 1-11, August.
    5. 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.
    6. Wenyuan Wang & Yuebao Wang & Ping Chen & Xueyuan Wu, 2022. "Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 924-965, September.
    7. Dalal Al Ghanim & Ronnie Loeffen & Alex Watson, 2018. "The equivalence of two tax processes," Papers 1811.01664, arXiv.org, revised Oct 2019.
    8. Ming, Ruixing & Wang, Wenyuan & Hu, Yijun, 2017. "On maximizing expected discounted taxation in a risk process with interest," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 128-140.
    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. Ewa Marciniak & Zbigniew Palmowski, 2018. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 533-552, November.
    11. Yin, Chuancun & Wen, Yuzhen, 2013. "Optimal dividend problem with a terminal value for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 769-773.
    12. 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.
    13. Hernández, Camilo & Junca, Mauricio & Moreno-Franco, Harold, 2018. "A time of ruin constrained optimal dividend problem for spectrally one-sided Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 57-68.
    14. Camilo Hernandez & Mauricio Junca & Harold Moreno-Franco, 2016. "A time of ruin constrained optimal dividend problem for spectrally one-sided L\'evy processes," Papers 1608.02550, arXiv.org, revised May 2017.
    15. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Papers 1605.04584, arXiv.org.
    16. Avanzi, Benjamin & Lau, Hayden & Wong, Bernard, 2020. "Optimal periodic dividend strategies for spectrally positive Lévy risk processes with fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 315-332.
    17. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 437-445.
    18. 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.
    19. 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.
    20. Zhenyu Cui, 2014. "Omega risk model with tax," Papers 1403.7680, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1910.08158. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.