Lorenzo Quirini | Searcharxiv

arXiv2026

Recovering Posterior Beliefs in Credit Risk: A Latent-State EM Extension of the Information-Geometric Framework

This paper develops a latent-state framework for recovering borrower-level posterior beliefs in credit-risk analysis. Creditworthiness and financial fragility are represented as latent dimensions, while observed borrower scores follow a finite Gaussian mixture model and default depends on the latent profile. Borrower-specific probabilities of default are obtained by averaging profile-specific default probabilities over the posterior distribution of latent states. A joint Expectation--Maximization procedure is used to estimate the mixture structure and the profile-specific default probabilities from observed score--default pairs. After estimation, predictive posterior beliefs are computed using the observed scores alone, thereby preserving the information available before default realization. A controlled simulation experiment evaluates the recovery of structural parameters, posterior beliefs, and borrower-level probabilities of default. Posterior distributions are interpreted as points on the probability simplex, and their recovery is assessed using both conventional error measures and information-geometric divergences. The results provide a controlled benchmark for studying the interaction between latent economic structure, posterior uncertainty, and credit-risk prediction.

q-fin.RM↗

arXiv2026

An Information-Geometric Framework for Bayesian Credit Risk Monitoring

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.

q-fin.RM↗