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Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

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Abstract

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest, in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent. Under some mild conditions, we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval. If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed, it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

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Acknowledgements

The authors would like to thank the anonymous referees for their insightful suggestions which have helped us improve the paper greatly.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Zai-ming Liu & Bing-zhen Geng

  2. School of Big Data and Statistics, Anhui University, Hefei, 230601, China

    Bing-zhen Geng & Shi-jie Wang

Authors
  1. Zai-ming Liu
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  2. Bing-zhen Geng
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  3. Shi-jie Wang
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Correspondence to Shi-jie Wang.

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Conflict of interest The authors declare no conflict of interest.

Additional information

Supported by the Natural Science Foundation of China(12071487, 11671404), the Natural Science Foundation of Anhui Province(2208085MA06), the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049, KJ2021A0060) and Hunan Provincial Innovation Foundation for Postgraduate(CX20200146).

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Liu, Zm., Geng, Bz. & Wang, Sj. Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims. Appl. Math. J. Chin. Univ. 39, 98–113 (2024). https://doi.org/10.1007/s11766-024-4213-6

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  • DOI: https://doi.org/10.1007/s11766-024-4213-6

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