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Large deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting times

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  • Gao, Qingwu
  • Lin, Jia’nan
  • Liu, Xijun

Abstract

In this paper, we consider a nonstandard compound renewal risk model with arbitrary dependence between the aggregate amount of claims caused by an accident and the waiting time of the corresponding accident. For the case when various dependence structures are imposed among the involved modeling factors and the common claim-size distribution is consistently varying tailed, we obtain for the large deviations of the aggregate amount of claims some asymptotic results, which hold uniformly for all x in a t-interval.

Suggested Citation

  • Gao, Qingwu & Lin, Jia’nan & Liu, Xijun, 2023. "Large deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting times," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s0167715223000330
    DOI: 10.1016/j.spl.2023.109809
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    References listed on IDEAS

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    1. Xijun Liu & Changjun Yu & Qingwu Gao, 2017. "Precise large deviations of aggregate claim amount in a dependent renewal risk model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2354-2363, March.
    2. Xijun Liu & Qingwu Gao & Ming Liu, 2020. "Large deviations for the stochastic present value of aggregate claims in the nonstandard compound renewal risk model with widely upper Orthant dependent claims," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(13), pages 3073-3093, July.
    3. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
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    5. Shen, Xinmei & Xu, Menghao & Mills, Ebenezer Fiifi Emire Atta, 2016. "Precise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk model," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 6-13.
    6. Chen, Yiqing & White, Toby & Yuen, Kam Chuen, 2021. "Precise large deviations of aggregate claims with arbitrary dependence between claim sizes and waiting times," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 1-6.
    7. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
    8. 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.
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    10. Kaas, Rob & Tang, Qihe, 2005. "A large deviation result for aggregate claims with dependent claim occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 251-259, June.
    11. Jiang, Tao & Cui, Sheng & Ming, Ruixing, 2015. "Large deviations for the stochastic present value of aggregate claims in the renewal risk model," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 83-91.
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