独立随机变量和的差的精细大偏差

发布时间：2018-06-19 17:47

  本文选题：精细大偏差 + 重尾　； 参考：《大连理工大学》2013年硕士论文

【摘要】：随着金融业的不断发展,保险已经成为了一个社会热点领域.现实的需要推动着保险业的理论水平不断提高,在这其中大偏差由于具有极深的理论水平和现实意义而吸引了 一大批优秀的研究者.早在1987年Bingham等数学家就在大偏差领域取得了卓有成效的成果,为大偏差领域今后的发展奠定了基石.在过去的10年间,关于大偏差的理论研究取得了突飞猛进的发展,其中又以唐启鹤和汪世界的工作最具代表性.在汪世界2004年的论文中,他将传统大偏差中一种保单的极限理论推广到了可数个不同保单.将大偏差的理论发展提高到了一个新的高度.自此众多的研究者都将研究的重点放在了不同保单的和的研究中,但在两种不同保单差的大偏差领域中确没有取得丝毫进展.基于这方面的考虑,本文重点研究不同保单之差的大偏差.具体来说,假设一家保险公司拥有两种不同的保单.第j次的索赔额记为{Xij,j≥1},i=1,2本文研究两种保单索赔和之间的非随机差和随机差即∑j=1n1(t) X1j-∑j=1n2(t) X2j和∑j=1N1(t) X1j-∑j=1n2(t) X2j,在这里ni(t)是正整数且当t→∞时,ni(t)→∞,i=1,2.Ni(t),i=1,2是索赔次数的计数过程.
[Abstract]:With the continuous development of the financial industry, insurance has become a hot social field. The need of reality promotes the theoretical level of insurance industry to improve constantly, in which large deviation attracts a large number of excellent researchers because of its deep theoretical level and practical significance. As early as 1987, mathematicians such as Bingham made fruitful achievements in the field of large deviations, which laid the foundation for the future development of the field of big deviations. In the past 10 years, the theoretical research on big deviation has made great progress, among which the work of Tang Qi-he and Wang World is the most representative. In Wang World's 2004 paper, he extended the limit theory of one policy in the traditional big deviation to several different policies. The development of the theory of big deviation has been raised to a new height. Since then, many researchers have focused on the sum of different policies, but no progress has been made in the big deviations between the two different policy gaps. Based on this consideration, this paper focuses on the large deviation of the difference between different policies. Specifically, suppose an insurance company has two different policies. In this paper, we study the nonrandom difference and random difference between two kinds of policy claims, that is 鈭，

本文编号：2040741