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Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model

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Abstract

Consider a two-dimensional renewal risk model, in which the claim sizes {\(\overrightarrow{X}_{k}\); k ≥ 1} form a sequence of i.i.d. copies of a non-negative random vector whose two components are dependent. Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d. random pairs, with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large. Then a precise large-deviation formula of the aggregate amount of claims is obtained.

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Acknowledgments

The authors thank the referees for pointing out some errors in a previous version, as well as for several comments that have led to improvements in this work.

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Authors and Affiliations

  1. Department of Statistics, Zhejiang University City College, Hangzhou, 310015, China

    Ke-ang Fu

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    **n-mei Shen

  3. Shunfeng Express, Shanghai, 200120, China

    Hui-jie Li

Authors
  1. Ke-ang Fu
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  2. **n-mei Shen
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  3. Hui-jie Li
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Corresponding author

Correspondence to Ke-ang Fu.

Additional information

This paper is supported by the National Social Science Foundation of China (No. 20BTJ050).

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Fu, Ka., Shen, Xm. & Li, Hj. Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model. Acta Math. Appl. Sin. Engl. Ser. 37, 539–547 (2021). https://doi.org/10.1007/s10255-021-1030-z

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  • DOI: https://doi.org/10.1007/s10255-021-1030-z

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