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Ruin probability in the presence of interest earnings and tax payments

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  • Wei, Li

Abstract

In this paper we investigate the ruin probability in a general risk model driven by a compound Poisson process. We derive a formula for the ruin probability from which the Albrecher-Hipp tax identity follows as a corollary. Then we study, as an important special case, the classical risk model with a constant force of interest and loss-carried-forward tax payments. For this case we derive an exact formula for the ruin probability when the claims are exponential and an explicit asymptotic formula when the claims are subexponential.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:1:p:133-138
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    References listed on IDEAS

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    1. Schmidli, Hanspeter, 2005. "On optimal investment and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 25-35, February.
    2. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
    3. Hao, Xuemiao & Tang, Qihe, 2008. "A uniform asymptotic estimate for discounted aggregate claims with subexponential tails," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 116-120, August.
    4. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    5. Konstantinides, Dimitrios & Tang, Qihe & Tsitsiashvili, Gurami, 2002. "Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 447-460, December.
    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.
    7. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
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    Citations

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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. 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.
    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. 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. 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. 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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