Far Eastern Mathematical Journal

To content of the issue


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


Q. H. Ďang, C. Su

2001, issue 1, Đ. 53ľ57


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.

Download the article (PDF-file)

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, ôProbability inequalities for sums of independent random variablesö, Teor. Verojatnost. i Primenen., 16 (1971), 660ľ675 (Russian).
[3] C. Kluppelberg and T. Mikosch, ôLarge deviations of heavy-tailed random sums with applications in insurance and financeö, J. Appl. Prob., 34 (1997), 293ľ308.
[4] C. Su, Q. H. Tang, T. Jiang, ôA Contribution to Large Deviations for Heavy-tailed Random Sumsö, Chinese Science, 44:2 (2001).
[5] Q. H. Tang, C. Su, T. Jiang and J. S. Zhang, ôLarge deviations for heavy-tailed random sums in compound renewal modelö, Stat. Prob. Letters, 52:1 (2001), 91ľ100.

To content of the issue