报告题目：A copula-based approximation to Markov chains
时 间：2024年12月26日（星期四）14:30
地 点：腾讯会议：678-480-927
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：The Markov chain is well studied and widely applied in many areas. For some Markov chains, it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is time-consuming for computation. In this paper, we propose an approximation method for Markov chains by applying the copula theory. For this purpose, we first discuss the checkerboard copula-based Markov chain, which is the Markov chain generated by the family of checkerboard copulas. This Markov chain has some appealing properties, such as self-similarity in copulas and having explicit forms of finite-dimensional distributions. Then we prove that each Markov chain can be approximated by a sequence of checkerboard copula-based Markov chains, and the error bounds of the approximate distributions are provided. Employing the checkerboard copula-based approximation method, we propose a sufficient condition for the geometric β-mixing of copula-based Markov chains. This condition allows copulas of Markov chains to be asymmetric. Finally, by applying the approximation method, analytical recurrence formulas are also derived for computing approximate distributions of both the first passage time and the occupation time of a Markov chain, and numerical results are listed to show the approximation errors.
报告人简介：杨静平，北京大学数学科学学院教授，博士生导师。主要研究方向包括金融和保险中的风险相依性、风险度量、信用风险管理以及资产支持证券等。在国际金融数学期刊Mathematical Finance, Finance and Stochastics、SIAM Journal on Financial Mathematics、Journal of Computational Finance、国际精算学期刊Insurance：Mathematics and Economics、ASTIN Bulletin、Scandinavian Actuarial Journal、North American Actuarial Journal等发表了多篇学术论文。主持完成了中国国债发行策略的随机模拟模型、国债收益率曲线的拟合、信贷资产证券化以及含权债估值模型等课题。