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Precise large deviation results for sums of sub-exponential claims in a size-dependent renewal risk model

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  • Shen, Xinmei
  • Xu, Menghao
  • Mills, Ebenezer Fiifi Emire Atta

Abstract

This paper deals with a size-dependent renewal risk model in which claim sizes and inter-occurrence times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure described via the conditional distribution of the inter-occurrence time given the subsequent claim size being large. The impact of this dependence structure on the tail behavior of aggregated claims is investigated and then a precise large deviation formula for the aggregate amount of sub-exponential claims is obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:114:y:2016:i:c:p:6-13
    DOI: 10.1016/j.spl.2016.03.002
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Baltrunas, Aleksandras & Leipus, Remigijus & Siaulys, Jonas, 2008. "Precise large deviation results for the total claim amount under subexponential claim sizes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1206-1214, August.
    4. Baltrunas, A. & Daley, D. J. & Klüppelberg, C., 2004. "Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 237-258, June.
    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.
    6. Tang, Qihe & Su, Chun & Jiang, Tao & Zhang, Jinsong, 2001. "Large deviations for heavy-tailed random sums in compound renewal model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 91-100, March.
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    Cited by:

    1. 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.
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    3. 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).
    4. Yuan, Meng & Lu, Dawei, 2022. "Precise large deviation for sums of sub-exponential claims with the m-dependent semi-Markov type structure," Statistics & Probability Letters, Elsevier, vol. 185(C).

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