An Information-Geometric Framework for Bayesian Credit Risk Monitoring

Abstract

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.