Bayesian Modeling for Uncertainty Management in Financial Risk Forecasting and Compliance

Abstract: A Bayesian analytics framework that precisely quantifies uncertainty offers a significant advance for financial risk management. We develop an integrated approach that consistently enhances the handling of risk in market volatility forecasting, fraud detection, and compliance monitoring. Our probabilistic, interpretable models deliver reliable results: We evaluate the performance of one-day-ahead 95% Value-at-Risk (VaR) forecasts on daily S&P 500 returns, with a training period from 2000 to 2019 and an out-of-sample test period spanning 2020 to 2024. Formal tests of unconditional (Kupiec) and conditional (Christoffersen) coverage reveal that an LSTM baseline achieves near-nominal calibration. In contrast, a GARCH(1,1) model with Student-t innovations underestimates tail risk. Our proposed discount-factor DLM model produces a slightly liberal VaR estimate, with evidence of clustered violations. Bayesian logistic regression improves recall and AUC-ROC for fraud detection, and a hierarchical Beta state-space model provides transparent and adaptive compliance risk assessment. The pipeline is distinguished by precise uncertainty quantification, interpretability, and GPU-accelerated analysis, delivering up to 50x speedup. Remaining challenges include sparse fraud data and proxy compliance labels, but the framework enables actionable risk insights. Future expansion will extend feature sets, explore regime-switching priors, and enhance scalable inference.