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Precise Large Deviations for Subexponential Distributions in a Multi Risk Model

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  • Dimitrios G. Konstantinides

    (Department of Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece)

Abstract

The precise large deviations asymptotics for the sums of independent identical random variables when the distribution of the summand belongs to the class S ∗ of heavy tailed distributions is studied. Under mild conditions, we extend the previous results from the paper Denisov et al. (2010) to asymptotics that are valid uniformly over some time interval. Finally, we apply the main result on the multi-risk model introduced by Wang and Wang (2007).

Suggested Citation

  • Dimitrios G. Konstantinides, 2018. "Precise Large Deviations for Subexponential Distributions in a Multi Risk Model," Risks, MDPI, vol. 6(2), pages 1-13, March.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:27-:d:138252
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    References listed on IDEAS

    as
    1. Yang Yang & Liwei Sha, 2016. "Precise large deviations for aggregate claims," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(10), pages 2801-2809, May.
    2. 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.
    3. 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.
    4. Predrag R. Jelenković & Petar Momčilović, 2004. "Large Deviations of Square Root Insensitive Random Sums," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 398-406, May.
    5. Lu, Dawei, 2012. "Lower bounds of large deviation for sums of long-tailed claims in a multi-risk model," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1242-1250.
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