Geodesic
On two broad classes of heavy-tailed distributions
Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 2, pp. 195-204.

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Since the introduction of Class $\mathcal M$ and Class $\mathcal M^*$, they have played important roles in insurance to describe tail equivalence of ruin probability and tail behavior of the deficit at ruin. And in insurance and finance most of heavy-tailed distributions with finite and positive expectations belong to Class $\mathcal M$. So it is important to study tail behaviors of Class $\mathcal M$ and Class $\mathcal M^*$. In this paper, we obtain some results on essential tail behaviors of these two classes. 
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Chun Su; Zhishui Hu. On two broad classes of heavy-tailed distributions. Dalʹnevostočnyj matematičeskij žurnal, Tome 5 (2004) no. 2, pp. 195-204. http://geodesic.mathdoc.fr/item/DVMG_2004_5_2_a3/

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