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Precise large deviation for sums of sub-exponential claims with the m-dependent semi-Markov type structure

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  • Yuan, Meng
  • Lu, Dawei

Abstract

Consider a renewal risk model in which the current inter-arrival time depends on a fixed number of previous claims but is independent of all other claims. We are interested in the precise large deviations of the aggregate amount of claims for the case of sub-exponential claims. In addition, an asymptotic estimate for the expectation of the aggregate amount of claims is also obtained. The asymptotic formulas are fully consistent with existing works in this study.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:185:y:2022:i:c:s016771522200044x
    DOI: 10.1016/j.spl.2022.109440
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    References listed on IDEAS

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    1. Asimit, Alexandru V. & Li, Jinzhu, 2018. "Systemic Risk: An Asymptotic Evaluation," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 673-698, May.
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2014. "Asymptotics for the ruin probability of a time-dependent renewal risk model with geometric Lévy process investment returns and dominatedly-varying-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 80-87.
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