两类熵风险度量的估计及渐近行为的研究

发布时间：2018-02-24 18:30

本文关键词： VaR CVaR SRM 熵风险度量偏差估计渐近行为　出处：《扬州大学》2015年硕士论文　论文类型：学位论文

【摘要】：在金融全球化的背景下,金融风险已成为国内外金融机构和监管部门共同关注的对象,金融风险管理技术也越来越受到人们的重视,而风险度量是金融风险管理的核心内容,因此对风险度量理论的研究具有重要的意义。到目前为止,国内外专家和学者们已经提出了VaR、CVaR、SRM、EVaR和熵风险度量等风险度量方法,为风险管理提供了可靠的理论支持,而近年来,将信息熵与风险度量理论相结合已经成为研究的热点。本文主要研究了复合泊松过程关于参数依赖于时间的凸熵风险度量和一致熵风险度量的偏差估计和渐近行为。本文的结构如下：第一章简要介绍了本课题的研究意义,并详细分析了风险度量理论的研究现状,引出本文的主要研究内容。第二章回顾了一些相关的基本理论知识。首先给出了大偏差原理、Varadhan定理和Gartner-Ellis定理,其次给出了复合泊松过程的定义和主要性质,并对一些性质作了必要的补充和证明,包括复合泊松过程的数学期望、方差以及指数矩等。第三章,首先对风险度量、凸风险度量和一致风险度量这几类风险度量进行了系统的总结和对比分析,然后介绍了VaR、CVaR、SRM和熵风险度量等几种常见的风险度量方法的定义、性质以及它们之间的关系,并以指数风险谱和几何风险谱为例,给出了关于谱风险度量的风险谱函数的构造方法。第四章是本文的主要研究内容。本文研究了复合泊松过程关于参数依赖于时间的凸熵风险度量和一致熵风险度量的偏差估计和渐近行为。首先给出凸熵风险度量在几种依赖于时间的参数下的一些偏差估计,以及通过大偏差理论得到了凸熵风险度量的一个渐近行为；其次还得到了一致熵风险度量的两个渐近行为。第五章,对整篇文章进行了总结和提出将来的工作。
[Abstract]:Under the background of financial globalization, financial risk has become the common concern of domestic and foreign financial institutions and regulators, and the technology of financial risk management has been paid more and more attention, and risk measurement is the core content of financial risk management. So it is of great significance to study the theory of risk measurement. Up to now, experts and scholars at home and abroad have put forward the risk measurement methods such as VaRCvar RNSRM VaR and entropy risk measurement, which provide reliable theoretical support for risk management, but in recent years, The combination of information entropy and risk measurement theory has become a hot topic in this paper. In this paper, we mainly study the deviation estimation and asymptotic behavior of the compound Poisson process on the parameter dependent convex entropy risk measurement and uniform entropy risk measurement. The structure of this paper is as follows: the first chapter briefly introduces the significance of this research. The present situation of risk measurement theory is analyzed in detail, and the main contents of this paper are introduced. In chapter 2, some basic theoretical knowledge is reviewed. Firstly, the large deviation theorem and Gartner-Ellis theorem are given. Secondly, the definition and main properties of compound Poisson process are given, and some properties are necessary to be supplemented and proved, including mathematical expectation, variance and exponential moment of compound Poisson process. Convex risk measurement and consistent risk measurement are systematically summarized and compared. Then, the definitions, properties and relationships of several common risk measurement methods, such as VaRN CVaRN SRM and entropy risk measurement, are introduced. Taking exponential risk spectrum and geometric risk spectrum as examples, In this paper, the method of constructing risk spectrum function about spectral risk measurement is given. Chapter 4th is the main content of this paper. In this paper, we study the convex entropy risk measure and uniform entropy risk degree of parametric dependent convex entropy in compound Poisson process. First, some deviation estimates of convex entropy risk measurement under several time-dependent parameters are given. An asymptotic behavior of convex entropy risk measurement is obtained by large deviation theory, and then two asymptotic behaviors of uniform entropy risk measurement are obtained. Chapter 5th summarizes the whole paper and puts forward the future work.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：F830.9;F224

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