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On maximizing expected discounted taxation in a risk process with interest

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  • Ming, Ruixing
  • Wang, Wenyuan
  • Hu, Yijun

Abstract

In risk theory, the problem of maximizing the expected cumulated discounted loss-carry-forward tax payments until ruin is a widely discussed topic since the taxation system was proposed by Albrecher and Hipp (2007). In the present paper, we discuss this maximization problem in the Cramér–Lundberg risk model including a constant force of interest. The optimal taxation return function is identified as the classical solution of the associated Hamilton–Jacobi–Bellman equation and the optimal taxation strategy in this risk model with interest is derived, which is of band type. Finally, an example is constructed for exponential claim sizes, in which closed-form expression for the optimal taxation return function is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:128-140
    DOI: 10.1016/j.spl.2016.11.004
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. 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.
    5. 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 & 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.

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