本文選題：精細(xì)大偏差 + 重尾�。� 參考：《大連理工大學(xué)》2013年碩士論文

【摘要】：隨著金融業(yè)的不斷發(fā)展,保險(xiǎn)已經(jīng)成為了一個(gè)社會(huì)熱點(diǎn)領(lǐng)域.現(xiàn)實(shí)的需要推動(dòng)著保險(xiǎn)業(yè)的理論水平不斷提高,在這其中大偏差由于具有極深的理論水平和現(xiàn)實(shí)意義而吸引了 一大批優(yōu)秀的研究者.早在1987年Bingham等數(shù)學(xué)家就在大偏差領(lǐng)域取得了卓有成效的成果,為大偏差領(lǐng)域今后的發(fā)展奠定了基石.在過(guò)去的10年間,關(guān)于大偏差的理論研究取得了突飛猛進(jìn)的發(fā)展,其中又以唐啟鶴和汪世界的工作最具代表性.在汪世界2004年的論文中,他將傳統(tǒng)大偏差中一種保單的極限理論推廣到了可數(shù)個(gè)不同保單.將大偏差的理論發(fā)展提高到了一個(gè)新的高度.自此眾多的研究者都將研究的重點(diǎn)放在了不同保單的和的研究中,但在兩種不同保單差的大偏差領(lǐng)域中確沒(méi)有取得絲毫進(jìn)展.基于這方面的考慮,本文重點(diǎn)研究不同保單之差的大偏差.具體來(lái)說(shuō),假設(shè)一家保險(xiǎn)公司擁有兩種不同的保單.第j次的索賠額記為{Xij,j≥1},i=1,2本文研究?jī)煞N保單索賠和之間的非隨機(jī)差和隨機(jī)差即∑j=1n1(t) X1j-∑j=1n2(t) X2j和∑j=1N1(t) X1j-∑j=1n2(t) X2j,在這里ni(t)是正整數(shù)且當(dāng)t→∞時(shí),ni(t)→∞,i=1,2.Ni(t),i=1,2是索賠次數(shù)的計(jì)數(shù)過(guò)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，

本文編號(hào)：2040741