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Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims

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  • Lu, Dawei
  • Zhang, Bin

Abstract

In this paper, a two-dimensional renewal risk model of insurance business with some strongly subexponential claim sizes is considered. Three types of the finite-time ruin probabilities under this model are discussed. We obtain the asymptotic upper and lower bounds for one type, and the asymptotic formulas for the others, which hold uniformly in a corresponding region, respectively.

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  • Lu, Dawei & Zhang, Bin, 2016. "Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 20-29.
    • Handle: RePEc:eee:stapro:v:114:y:2016:i:c:p:20-29
    DOI: 10.1016/j.spl.2016.03.005
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    References listed on IDEAS

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    1. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2006. "On the first time of ruin in the bivariate compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 298-308, April.
    2. Li, Junhai & Liu, Zaiming & Tang, Qihe, 2007. "On the ruin probabilities of a bidimensional perturbed risk model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 185-195, July.
    3. Leipus, Remigijus & Siaulys, Jonas, 2007. "Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 498-508, May.
    4. Baltrunas, Aleksandras & Leipus, Remigijus & Siaulys, Jonas, 2008. "Precise large deviation results for the total claim amount under subexponential claim sizes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1206-1214, August.
    5. Baltrunas, A. & Daley, D. J. & Klüppelberg, C., 2004. "Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 237-258, June.
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    Cited by:

    1. Dawei Lu & Meng Yuan, 2022. "Asymptotic Finite-Time Ruin Probabilities for a Bidimensional Delay-Claim Risk Model with Subexponential Claims," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2265-2286, December.
    2. Shijie Wang & Yueli Yang & Yang Liu & Lianqiang Yang, 2023. "Asymptotics for a Bidimensional Renewal Risk Model with Subexponential Main Claims and Delayed Claims," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-13, September.

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