Far Eastern Mathematical Journal

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Note on large deviations for heavy-tailed random sums in compound renewal model


Q. H. Тang, C. Su

2001, issue 1, P.


Abstract
In this note we investigate the precise large deviations for heavy-tailed random sums in compound renewal risk model and obtain a result which improves the related results in [5]. The proof is very simple, which shows that in some cases the compound renewal risk model can be reduced to the ordinary renewal one.

Keywords:
Compound Renewal Risk Model, Extended Regular Variation, Subexponential Distribution, Large Deviations.

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References

[1] P. Embrechts, C. Kluppelberg and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997.
[2] D. H. Fuc and S. V. Nagaev, “Probability inequalities for sums of independent random variables”, Teor. Verojatnost. i Primenen., 16 (1971), 660–675 (Russian).
[3] C. Kluppelberg and T. Mikosch, “Large deviations of heavy-tailed random sums with applications in insurance and finance”, J. Appl. Prob., 34 (1997), 293–308.
[4] C. Su, Q. H. Tang, T. Jiang, “A Contribution to Large Deviations for Heavy-tailed Random Sums”, Chinese Science, 44:2 (2001).
[5] Q. H. Tang, C. Su, T. Jiang and J. S. Zhang, “Large deviations for heavy-tailed random sums in compound renewal model”, Stat. Prob. Letters, 52:1 (2001), 91–100.

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