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Large deviations for sums of claims in a general renewal risk model with the regression dependent structure

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  • Li, Rong
  • Bi, Xiuchun
  • Zhang, Shuguang

Abstract

The regression dependence is a practical dependent structure which provides a good mechanism to describe non-life insurance businesses, and further allows applications in various areas. In this paper, we investigate large deviations for random sums of extended negatively dependent random variables in the general renewal risk model with the regression size-dependent structure. For heavy-tailed distributions of consistently-varying tailed, we obtain the large deviation formulas.

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  • Li, Rong & Bi, Xiuchun & Zhang, Shuguang, 2020. "Large deviations for sums of claims in a general renewal risk model with the regression dependent structure," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301607
    DOI: 10.1016/j.spl.2020.108857
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    References listed on IDEAS

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    1. Shen, Xinmei & Zhang, Yi, 2012. "Moderate deviations for a risk model based on the customer-arrival process," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 116-122.
    2. Ke-Ang Fu & Xinmei Shen, 2017. "Moderate deviations for sums of dependent claims in a size-dependent renewal risk model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3235-3243, April.
    3. 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.
    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. Cossette, Hélène & Marceau, Etienne & Marri, Fouad, 2008. "On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 444-455, December.
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    Cited by:

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    2. Fu, Ke-Ang & Liu, Yang & Wang, Jiangfeng, 2022. "Precise large deviations in a bidimensional risk model with arbitrary dependence between claim-size vectors and waiting times," Statistics & Probability Letters, Elsevier, vol. 184(C).

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