椭圆分布的同单调性及其应用
发布时间：2018-08-13 20:32
【摘要】：在传统的风险理论中,一个投资组合的各个风险之间是被假定为相互独立的.但是,一般来讲,每个向量本身都有相依的成分.像在雾天里,同一地区的所有车辆被卷入事故里的概率都很大.在干燥的夏天,所有的木制房屋都更有可能发生火灾.在相同地方,地震和火灾的索赔之间是相关的,尽管严格来讲每个索赔不可预测.还有养老金,他们在同一个公司工作,乘坐相同的航班,那么这些人的死亡率在一定程度上是相依的.所以研究同单调对于更好的预测风险具有非常重要的现实意义.本文主要研究同单调和,共分五章.本文第一章是绪论,主要介绍了几个具有相依性的现实例子,以及同单调研究的背景和意义.第二章第一部分主要介绍了分布函数、逆分布函数的定义以及相关性质、定理,第二部分介绍了同单调性的概念以及相关定理.第三章第一部分介绍了同单调和的定义及相关定理,并举出了几个同单调和(积)的封闭性的例子,并且进一步得出椭圆分布具有同单调和的封闭性,对数椭圆分布具有同单调积的封闭性.举了一个离散的例子:几何分布并不满足同单调和的封闭性.因此得到结论,并不是所有分布都满足同单调和(积)的封闭性.在第四章主要介绍了相关序的定义及几个定理结果.第五章是总结及展望.
[Abstract]:In traditional risk theory, each risk of a portfolio is assumed to be independent of each other. Generally speaking, however, each vector itself has a dependent component. Like in foggy weather, all vehicles in the same area are likely to be involved in accidents. In dry summer, all wooden houses are more likely to fire. In the same place, there is a correlation between earthquake and fire claims, although each claim is strictly unpredictable. And pensions, where they work in the same company and take the same flights, their mortality rates are somewhat dependent. Therefore, the study of the same monotone is of great practical significance for better prediction of risk. This paper mainly studies the same monotone sum, which is divided into five chapters. The first chapter is an introduction, which mainly introduces several practical examples with dependence, and the background and significance of the same monotone research. The first part introduces the definition of distribution function, the definition of inverse distribution function and its related properties, theorems. The second part introduces the concept of homotonicity and related theorems. In chapter three, we introduce the definition of homomorphism and some related theorems, and give some examples of closure of homotonicity sum (product). Furthermore, we obtain that elliptic distribution has the closed property of homoharmonic. The logarithmic elliptic distribution has the closed property of the same monotone product. A discrete example is given: the geometric distribution does not satisfy the closed property of homoharmonic. Therefore, it is concluded that not all distributions satisfy the closure of the same monotone sum (product). In chapter 4, we mainly introduce the definition of related order and some theorems. The fifth chapter is the summary and prospect.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224
本文编号：2182104
[Abstract]:In traditional risk theory, each risk of a portfolio is assumed to be independent of each other. Generally speaking, however, each vector itself has a dependent component. Like in foggy weather, all vehicles in the same area are likely to be involved in accidents. In dry summer, all wooden houses are more likely to fire. In the same place, there is a correlation between earthquake and fire claims, although each claim is strictly unpredictable. And pensions, where they work in the same company and take the same flights, their mortality rates are somewhat dependent. Therefore, the study of the same monotone is of great practical significance for better prediction of risk. This paper mainly studies the same monotone sum, which is divided into five chapters. The first chapter is an introduction, which mainly introduces several practical examples with dependence, and the background and significance of the same monotone research. The first part introduces the definition of distribution function, the definition of inverse distribution function and its related properties, theorems. The second part introduces the concept of homotonicity and related theorems. In chapter three, we introduce the definition of homomorphism and some related theorems, and give some examples of closure of homotonicity sum (product). Furthermore, we obtain that elliptic distribution has the closed property of homoharmonic. The logarithmic elliptic distribution has the closed property of the same monotone product. A discrete example is given: the geometric distribution does not satisfy the closed property of homoharmonic. Therefore, it is concluded that not all distributions satisfy the closure of the same monotone sum (product). In chapter 4, we mainly introduce the definition of related order and some theorems. The fifth chapter is the summary and prospect.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224
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