Geodesic
Note on large deviations for heavy-tailed random sums in compound renewal model
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 1, pp. 53-57 
Q. H. Тang; C. Su. Note on large deviations for heavy-tailed random sums in compound renewal model. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 1, pp. 53-57. http://geodesic.mathdoc.fr/item/DVMG_2001_2_1_a3/
@article{DVMG_2001_2_1_a3,
     author = {Q. H. {\CYRT}ang and C. Su},
     title = {Note on large deviations for heavy-tailed random sums in compound renewal model},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {53--57},
     year = {2001},
     volume = {2},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2001_2_1_a3/}
}
TY  - JOUR
AU  - Q. H. Тang
AU  - C. Su
TI  - Note on large deviations for heavy-tailed random sums in compound renewal model
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2001
SP  - 53
EP  - 57
VL  - 2
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2001_2_1_a3/
LA  - en
ID  - DVMG_2001_2_1_a3
ER  - 
%0 Journal Article
%A Q. H. Тang
%A C. Su
%T Note on large deviations for heavy-tailed random sums in compound renewal model
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2001
%P 53-57
%V 2
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2001_2_1_a3/
%G en
%F DVMG_2001_2_1_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] P. Embrechts, C. Klüppelberg and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997 | MR | Zbl

[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) | MR

[3] C. Klüppelberg and T. Mikosch, “Large deviations of heavy-tailed random sums with applications in insurance and finance”, J. Appl. Prob., 34 (1997), 293–308 | DOI | MR | Zbl

[4] C. Su, Q. H. Tang, T. Jiang, “A Contribution to Large Deviations for Heavy-tailed Random Sums”, Chinese Science, 44:2 (2001) | MR

[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 | DOI | MR | Zbl