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Asymptotic Finite-Time Ruin Probabilities for a Bidimensional Delay-Claim Risk Model with Subexponential Claims

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  • Dawei Lu

    (Dalian University of Technology
    Dalian University of Technology)

  • Meng Yuan

    (Dalian University of Technology)

Abstract

This paper considers a bidimensional delay-claim risk model with constant force of interest, in which each main claim may induce a delayed claim after a random time. Specifically, if the main claims and delayed claims follow the subexponential distributions with some dependence structure, we obtain some precise asymptotic estimates for the finite-time ruin probabilities. In addition, some numerical simulations are presented to test the performance of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-021-09921-2
    DOI: 10.1007/s11009-021-09921-2
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    References listed on IDEAS

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    1. Li, Jinzhu, 2013. "On pairwise quasi-asymptotically independent random variables and their applications," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2081-2087.
    2. Yang, Haizhong & Li, Jinzhu, 2019. "On asymptotic finite-time ruin probability of a renewal risk model with subexponential main claims and delayed claims," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 153-159.
    3. Chen, Yiqing, 2020. "A Kesten-type bound for sums of randomly weighted subexponential random variables," Statistics & Probability Letters, Elsevier, vol. 158(C).
    4. Xiao, Yuntao & Guo, Junyi, 2007. "The compound binomial risk model with time-correlated claims," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 124-133, July.
    5. 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.
    6. Xie, Jie-hua & Zou, Wei, 2010. "Expected present value of total dividends in a delayed claims risk model under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 415-422, April.
    7. Fengyang Cheng & Dongya Cheng, 2018. "Randomly weighted sums of dependent subexponential random variables with applications to risk theory," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(3), pages 191-202, March.
    8. Yuen, K. C. & Guo, J. Y., 2001. "Ruin probabilities for time-correlated claims in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 47-57, August.
    9. 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.
    10. Waters, Howard R. & Papatriandafylou, Alex, 1985. "Ruin probabilities allowing for delay in claims settlement," Insurance: Mathematics and Economics, Elsevier, vol. 4(2), pages 113-122, April.
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    Cited by:

    1. Dan Zhu & Ming Zhou & Chuancun Yin, 2023. "Finite-Time Ruin Probabilities of Bidimensional Risk Models with Correlated Brownian Motions," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    2. Yuan, Meng & Lu, Dawei, 2023. "Asymptotics for a time-dependent by-claim model with dependent subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 120-141.
    3. 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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