基于熵优化原理的大偏差风险分析与应用研究

项目名称： 基于熵优化原理的大偏差风险分析与应用研究

项目编号： No.71301015

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 管理科学

项目作者： 姜昱汐

作者单位： 大连交通大学

项目金额： 18万元

中文摘要： 风险分析的一个难题是无法给出准确描述不完全信息下尖峰厚尾分布风险特征的简便方法。本课题基于熵优化原理，提出一种求解大偏差中率函数和矩母函数的新方法，并作为尖峰厚尾分布的风险分析工具，应用到风险管理的四个方面。课题的研究分为理论研究和应用研究两部分：在理论研究中，一是从叉熵函数和率函数的等价关系入手，基于熵优化原理构建优化模型，导出率函数，进而得到大偏差中损失分布的尾部概率；二是从叉熵函数同矩母函数的Fenchel对偶关系入手，基于熵优化原理构建优化模型，导出大偏差中的矩母函数。在应用研究中，采用理论研究结果，构建计算破产概率、保费定价、组合贷款违约率和组合贷款定价的优化模型，并进行实证分析，计算不完全信息条件下盈余过程的破产概率、保费定价、不同信用等级下的组合贷款违约率和组合贷款定价。本课题致力于提供一种大偏差风险分析的简便方法，对大偏差理论的应用推广和尖峰厚尾的风险分析研究具有重要作用。

中文关键词： 熵优化方法；大偏差原理；重要性抽样；风险度量；尾部概率

英文摘要： It is very difficult to propose a method that can measure the the risk with excess kurtosis and heavy tail accurately and simply. Based on the entropy optimizaiton principle, this project will study a new method to solve the rate function and moment generating function of large deviation. Using it, the method will be applied to measure the risk with excess kurtosis and heavy tail in the four fields of risk management. The research of the project includes the theoretical and application. There are two step in the theoretical research. Firstly, based on the entropy optimization function, the rate function will be derived by the equavilence relation and the tail probability of loss distribution of large deviation can be given. Secondly, the moment generating function can be derived from the Fenchel dual relation between cross-entropy function and moment generating function. Based on the results of the theoretical and application researches, the optimizaiton models will be proposed to calculate ruin probability, insurance premium pricing, default rate and pricing for loan portfolio. Using the models, the expirical analysis are studied to calculated the ruin probability, insurance premium pricing with imperfect information, the default rate and pricing for loan portfolio with different credict levels. The objective

英文关键词： Entropy optimizaiton method；Large deviation principle；Importance Sampling；Risk Measure；Tail probability