Dynamic Credit Decision-Making with Continuous Risk Preference: A Unified Framework of Entropy-Regularized HJB and Soft Actor-Critic

Traditional credit scoring treats lending as static classification and lacks the ability to adjust risk preferences dynamically. This paper develops a dynamic credit decision framework based on the entropy-regularized Hamilton–Jacobi–Bellman (ER-HJB) equation. Theoretically, we prove the existence and uniqueness of a solution to the ER-HJB equation, show that under exact tabular assumptions the soft policy iteration underlying Soft Actor-Critic (SAC) converges to this solution, and derive a closed-form analytical solution under linear-quadratic conditions. Empirically, using LendingClub loan panel data (2016–2018), we show that a single entropy coefficient continuously modulates the risk–return trade-off. As this coefficient increases from 0.01 to 1.00, tail risk (CVaR 95%) steadily improves, while the Sortino ratio peaks near 0.20. The dynamic SAC model outperforms static baselines (logistic regression, XGBoost, LightGBM) in average reward and, by tuning the entropy coefficient, achieves significant downside risk reduction without retraining. This framework transforms credit scoring into dynamic optimal control with continuously adjustable and interpretable risk preferences, offering a theoretically grounded tool for refined risk management.