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Precise large deviation results for the total claim amount under subexponential claim sizes

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  • Baltrunas, Aleksandras
  • Leipus, Remigijus
  • Siaulys, Jonas

Abstract

The paper deals with the renewal risk model. A precise large deviation result in the case of subexponential claim sizes is proved. As a special case, the example of Pareto distributed claim sizes and inter-occurrence times is investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1206-1214
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    References listed on IDEAS

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    1. 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.
    2. 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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    Citations

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    Cited by:

    1. 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.
    2. Lu, Dawei, 2011. "Lower and upper bounds of large deviation for sums of subexponential claims in a multi-risk model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1911-1919.
    3. Yiqing Chen & Kam C. Yuen & Kai W. Ng, 2011. "Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 821-833, December.
    4. Lu, Dawei & Zhang, Bin, 2016. "Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 20-29.
    5. 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).
    6. 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.
    7. Remigijus Leipus & Jonas Šiaulys, 2009. "Asymptotic behaviour of the finite‐time ruin probability in renewal risk models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 309-321, May.

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