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The equivalence of two tax processes

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  • Al Ghanim, Dalal
  • Loeffen, Ronnie
  • Watson, Alexander R.

Abstract

We introduce two models of taxation, the latent and natural tax processes, which have both been used to represent loss-carry-forward taxation on the capital of an insurance company. In the natural tax process, the tax rate is a function of the current level of capital, whereas in the latent tax process, the tax rate is a function of the capital that would have resulted if no tax had been paid. Whereas up to now these two types of tax processes have been treated separately, we show that, in fact, they are essentially equivalent. This allows a unified treatment, translating results from one model to the other. Significantly, we solve the question of existence and uniqueness for the natural tax process, which is defined via an integral equation. Our results clarify the existing literature on processes with tax.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:90:y:2020:i:c:p:1-6
    DOI: 10.1016/j.insmatheco.2019.10.002
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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