用于贝叶斯信用风险监测的信息几何框架
An Information-Geometric Framework for Bayesian Credit Risk Monitoring
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中文总结 AI 辅助
该研究提出一种信息几何框架，以贝叶斯方法结合线性-高斯设定，利用Kullback-Leibler等散度实现信用风险监测与投资组合细分比较，为信用监测提供几何解释。
中文摘要 AI 辅助
我们提出一种用于信用风险监测的信息几何框架，其中银行对借款人的认知由关于信用可靠性和财务脆弱性潜在维度的后验分布表示。在线性-高斯设定下，贝叶斯更新将观测到的行为评分映射为高斯后验信念，这些信念构成了配备费舍尔信息度量的统计流形。在协方差相同的情况下，诱导几何简化为后验均值上的马氏度量；而针对借款人的协方差矩阵则使信息距离能够同时考虑预期风险和评估不确定性。模拟实验展示了如何使用Kullback-Leibler散度和Jeffreys散度来比较投资组合细分部分。该框架为信用监测提供了几何解释，将其视为借款人风险后验信念的演化过程。
英文摘要
We propose an information-geometric framework for credit risk monitoring in which a bank's knowledge of a borrower is represented by a posterior distribution over latent dimensions of creditworthiness and financial fragility. Under a linear-Gaussian specification, Bayesian updating maps observed behavioural scores into Gaussian posterior beliefs, which form a statistical manifold endowed with the Fisher information metric. In the common-covariance case, the induced geometry reduces to the Mahalanobis metric on posterior means, while borrower-specific covariance matrices allow informational distances to account for both expected risk and assessment uncertainty. Simulation exercises illustrate how Kullback-Leibler and Jeffreys divergences can be used to compare portfolio segments. The framework provides a geometric interpretation of credit monitoring as the evolution of posterior beliefs over borrower risk.
