On two broad classes of heavy-tailed distributions

Chun Su, Zhishui Hu

2004, 2, . 195204

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.

class $\mathcal{M}$, class $\mathcal{M^?}$, class $\mathcal{D}$, tail behaviors

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