Abstract
We investigate precise large deviations for heavy-tailed random sums. We prove a general asymptotic relation in the compound renewal risk model for consistently varying-tailed distributions. This model was introduced in [Q. Tang, C. Su, T. Jiang, and J.S. Zang, Large deviation for heavy-tailed random sums in compound renewal model, Stat. Probab. Lett., 52:91–100, 2001] as a more practical risk model. The proof is based on the inequality found in [D. Fuk and S.V. Nagaev, Probability for sums of independent random variables, Theory Probab. Appl., 16:600–675, 1971].
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Konstantinides, D.G., Loukissas, F. Precise large deviations for consistently varying-tailed distributions in the compound renewal risk model. Lith Math J 50, 391–400 (2010). https://doi.org/10.1007/s10986-010-9094-0
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DOI: https://doi.org/10.1007/s10986-010-9094-0