Bayesian Modeling for Uncertainty Management in Financial Risk Forecasting and Compliance

2025-12-06

AI Summary

This study addresses three critical challenges in financial risk management: insufficient uncertainty quantification, poor model interpretability, and inadequate real-time performance. Methodologically, it introduces a unified Bayesian analytical framework comprising: (1) a discount-factor-augmented Dynamic Linear Model (DLM) for adaptive Value-at-Risk (VaR) calibration; (2) a hierarchical Beta state-space model enabling interpretable, adaptive compliance risk assessment; and (3) a hybrid Bayesian logistic regression–LSTM–GARCH(1,1)–Student-*t* architecture for enhanced fraud detection. Empirical results demonstrate that VaR forecasts pass rigorous Kupiec and Christoffersen backtests; fraud detection achieves significantly improved AUC and recall; compliance assessments provide full posterior interpretability; and GPU-accelerated Monte Carlo inference accelerates end-to-end analysis by 50×. The core contribution is a probabilistic, adaptive, and scalable Bayesian risk engine that jointly models heterogeneous risk tasks—marking a paradigm shift toward integrated, uncertainty-aware financial risk analytics.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Develops Bayesian models for financial risk forecasting and compliance
• Quantifies uncertainty in market volatility and fraud detection
• Enhances interpretability and speed in risk management analytics

Innovation

• Bayesian framework quantifies uncertainty for financial risk
• Probabilistic models improve forecasting, fraud detection, and compliance
• GPU acceleration enables up to 50x faster analysis speed