Applications of Nonstandard Analysis in Economics, Probability and Statistics

发布时间:2022-09-19 浏览次数:10




报告题目:Applications of Nonstandard Analysis in Economics, Probability and Statistics


Nonstandard analysis, a powerful machinery derived from mathematical logic, has had many applications in various areas of mathematics such as probability theory, stochastic processes, mathematical physics, functional analysis, and mathematical economics. Nonstandard analysis allows construction of a single object—a hyperfinite probability space—which satisfies all the first order logical properties of a finite probability space, but which can be simultaneously viewed as a measure theoretical probability space via the Loeb construction. As a consequence, the hyperfinite/measure duality has proven to be particularly in porting discrete results into their continuous settings. We present two applications of this novel approach:

(1) Extending the stable matching lemma to the infinite markets setting;

(2) Existence of Walrasian equilibrium for production economy models that are specific to climate change.

Finally, we breifly discuss other applications of nonstandard analysis to Markov processes, statistical decision theory and economic dynamics.



端木昊随博士,现为哈尔滨工业大学数学研究院长聘教授,博士生导师。他2017年毕业于多伦多大学并获统计学博士学位,于2018-2021在加州大学伯克利分校师从著名经济学家Robert Anderson 进行博士后研究,并于2021年入选国家高层次人才计划。他的主要研究方向是非标准分析及其在概率(主要是马尔可夫链),统计(主要是统计决策理论)和经济学(主要是一般均衡理论和经济动态理论)中的应用。他的论文发表于Mem. Amer. Math. SocAnn. Stat等国际著名期刊。




版权所有 Copyright © 2012 苏州大学金融工程研究中心. 访问次数: