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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     author = {Chun Su and Zhishui Hu},
     title = {On two broad classes of heavy-tailed distributions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     volume = {5},
     number = {2},
     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/DVMG_2004_5_2_a3/}
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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/