一类重尾分布下的随机游动的渐近结果及其在风险理论中的应用

Some Asymptotic Results about a Kind of Heavy-tailed Random Walk with Application in Risk Theory

定义了一类新的重尾分布族L^＊（m）,并研究了该分布族的若干性质,讨论了在该类分布族下的（非标准）随机游动{Sn}的尾概率的渐近性质,并给出了在风险理论中的应用.

This paper introduced a new class L^＊（m） of heavy-tailed distribution functions, some properties about it axe studied. Under the assumption that the distributions of the summands of a （non-standard） random walk {Sn}n≥0 belong to L^＊（m） we obtain the asymptotic estimate for the distribution of maximum of {Sn}n≥0. Application in risk theory is investigated.