概率测度间差异性度量方法与不确定性及金融经济学应用  

A method of measuring the difference between probability models as uncertainty and its applications in financial economics

作　　者：张丽宏 林海嵩 王浩[1] Lihong Zhang;Haisong Lin;Hao Wang

机构地区：[1]清华大学经济管理学院,北京100084

出　　处：《中国科学：数学》2021年第11期1933-1954,共22页Scientia Sinica：Mathematica

基　　金：清华大学自主科研计划(批准号:2021THZWJC28)资助项目。

摘　　要：针对在Knight不确定性下的决策问题,本文基于非参数化的思想提出了一种新的概率模型之间差异的度量方法,以此规避参数化不确定性模型描述金融数据特征的损失.该度量方法对概率模型的形式没有限制,并且易于计算.在正态假设下,使用该度量方法的非参数化检验方法可以退化为一种更不易犯第一类错误的参数检验方法.本文将该度量方法应用于美国标准普尔500指数,发现了不确定性指标的双波峰特征,结果表明概率模型之间的差异捕捉到了独特的信息并且在金融市场中可能有特别的预警作用.本文得到的不确定性指标也可以被应用于研究不确定性与资产定价的关系.We develop a novel methodology to measure the difference between probability models.Unlike the parametric approach,this non-parametric approach can describe complex financial data without being limited to the uncertainty about specific moments or parameters.It can be applied to various probability distributions and is easy to use.For the special case of normal distributions,our method can be simplified to a parametric method which is less likely to make the type I error.Applying the technique to the S&P500 index,we find that our uncertainty measure displays a dual-peak feature and conveys distinct information to play a significant alarming role.The measure can also be applied to study the relationship between uncertainty and asset pricing.

关 键 词：概率测度 KNIGHT不确定性 模糊性 金融 资产定价 

分 类 号：F831.51[经济管理—金融学] F224