An Information-Geometric Framework for Bayesian Credit Risk Monitoring

Battle Count: 85

The paper is focused on credit risk monitoring for banking institutions rather than quantitative trading. However, the information-geometric framework and divergence measures could potentially be adapted for portfolio risk assessment in trading contexts. The Bayesian updating and manifold-based representation of uncertainty are conceptually transferable but the paper's direct application is to lending and credit portfolio management, not trading strategies or market-making.

The core Bayesian updating in the linear-Gaussian case is straightforward (standard conjugate Gaussian formulas). However, the information-geometric layer (Fisher metric computation, natural/expectation coordinate transformations, KL and Jeffreys divergences on the full Gaussian manifold) requires familiarity with differential geometry and exponential family theory. The borrower-specific covariance extension adds complexity with the block-structured Hessian and the two-component line element. The R implementation is relatively simple (MASS package), but understanding and extending the geometric framework requires significant mathematical background.

All simulations use synthetic data generated with a fixed random seed. Accompanying R scripts are provided as ancillary files requiring only the MASS package. The scripts can be executed independently. However, no real-world data or external repository URL is provided, and the model parameters (A, Sigma, m(z), P(z)) are specified exogenously.