常利率扰动复合Poisson风险模型的大偏差及其应用

发布时间：2018-09-19 21:07

【摘要】：金融风险管理中的模型建设具有重要意义,为了更好的管控风险,需要将经典模型不断的发展优化。本文的主要工作建立在经典风险模型的基础之上,考虑对带利率和扰动这两方面推广模型的研究。因为大偏差工具能够对极端索赔问题进行较好的量化,所以我们把工作的重心放在大偏差原理对风险过程的估计上。本文分为如下几个章节:第一章首先介绍了经典风险模型以及相关的重要结论,在经典模型中增加利率和随机扰动因素,得到本文所关注的常利息扰动复合泊松风险模型;然后给出几类风险模型极限性质的研究结果;最后阐述本文的主要工作。第二章主要介绍本文相关的基础知识。我们给出一些基本概念和重要的定理,包括泊松散粒噪声、Ito公式、大偏差的定义、测度对数变换、Cramer定理、Gartner-Ellis定理、Varadhan定理以及熵风险度量等。第三章是本文的主要研究结果。我们首先证明了 Cramer-Lundberg风险模型满足大偏差原理,得到该盈余过程的渐近性质;然后讨论常利率扰动模型,对比现值与折现值索赔的差异过程,证明了差异过程满足大偏差原理;最后,给出Varadhan定理并研究它在熵风险度量上的应用,得到了熵风险度量的极限估计,从而得到熵风险度量极限行为的一个刻画。第四章是论文工作的总结与展望。
[Abstract]:Model building in financial risk management is of great significance. In order to better manage risk, it is necessary to develop and optimize the classical model. The main work of this paper is based on the classical risk model, considering the generalized model with interest rate and perturbation. Because the large deviation tool can well quantify the extreme claim problem, we focus our work on the estimation of the risk process based on the large deviation principle. This paper is divided into the following chapters: the first chapter introduces the classical risk model and related important conclusions, add interest rate and stochastic perturbation factors in the classical model, get the constant interest disturbance complex Poisson risk model; Then the research results of the limit properties of several kinds of risk models are given, and the main work of this paper is expounded. The second chapter mainly introduces the basic knowledge of this paper. We give some basic concepts and important theorems, including Ito formula for loose particle noise, definition of large deviation, Cramer theorem of measure logarithmic transformation, Gartner-Ellis theorem and Varadhan theorem, and entropy risk measurement. The third chapter is the main research results of this paper. We first prove that the Cramer-Lundberg risk model satisfies the large deviation principle and obtain the asymptotic property of the surplus process, then discuss the constant interest rate perturbation model, compare the difference process between the present value and the discounted value claim, and prove that the difference process satisfies the large deviation principle. Finally, the Varadhan theorem is given and its application in entropy risk measurement is studied. The limit estimation of entropy risk measurement is obtained, and a characterization of the limit behavior of entropy risk measurement is obtained. The fourth chapter is the summary and prospect of the thesis.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F822.0

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