Credit Scoring

Statistical fairness metrics in AI-driven credit decisions conflate two causally distinct mechanisms: discrimination operating directly from a protected attribute to a credit outcome, and structural inequality propagating through legitimate financial features. We formalise this distinction using Pearl's framework of natural direct and indirect effects applied to the credit decision setting. Our primary theoretical contribution is an identification strategy for natural direct and indirect effects under treatment-induced confounding -- the prevalent setting in which protected attributes causally affect both financial mediators and the final decision, violating standard sequential ignorability. We show that interventional direct and indirect effects (IDE/IIE) are identified under the weaker Modified Sequential Ignorability assumption, and prove that IDE/IIE provide conservative bounds on the unidentified natural effects under monotone indirect treatment response. We propose a doubly-robust augmented inverse probability weighted (AIPW) estimator for IDE/IIE with semiparametric efficiency properties, implemented via cross-fitting. An E-value sensitivity analysis addresses residual confounding on the direct pathway. Empirical evaluation on 89,465 real HMDA conventional purchase mortgage applications from New York State (2022) demonstrates that approximately 77% of the observed 7.9 percentage-point racial denial disparity operates through financial mediators shaped by structural inequality, while the remaining 23% constitutes a conservative lower bound on direct discrimination. The open-source CausalFair Python package implements the full pipeline for deployment at resource-constrained financial institutions.

We propose a semi-structured discrete-time multi-state model to analyse mortgage delinquency transitions. This model combines an easy-to-understand structured additive predictor, which includes linear effects and smooth functions of time and covariates, with a flexible neural network component that captures complex nonlinearities and higher-order interactions. To ensure identifiability when covariates are present in both components, we orthogonalise the unstructured part relative to the structured design. For discrete-time competing transitions, we derive exact transformations that map binary logistic models to valid competing transition probabilities, avoiding the need for continuous-time approximations. In simulations, our framework effectively recovers structured baseline and covariate effects while using the neural component to detect interaction patterns. We demonstrate the method using the Freddie Mac Single-Family Loan-Level Dataset, employing an out-of-time test design. Compared with a structured generalised additive benchmark, the semi-structured model provides modest but consistent gains in discrimination across the earliest prediction spans, while maintaining similar Brier scores. Adding macroeconomic indicators provides limited incremental benefit in this out-of-time evaluation and does not materially change the estimated borrower-, loan-, or duration-driven effects. Overall, semi-structured multi-state modelling offers a practical compromise between transparent effect estimates and flexible pattern learning, with potential applications beyond credit-transition forecasting.

Accurate prediction of loan defaults is a central challenge in credit risk management, particularly in modern financial datasets characterised by nonlinear relationships, class imbalance, and evolving borrower behaviour. Traditional statistical models and static ensemble methods often struggle to maintain reliable performance under such conditions. This study proposes an Optimised Greedy-Weighted Ensemble framework for loan default prediction that dynamically allocates model weights based on empirical predictive performance. The framework integrates multiple machine learning classifiers, with their hyperparameters first optimised using Particle Swarm Optimisation. Model predictions are then combined via a regularised greedy weighting mechanism. At the same time, a neural-network-based meta-learner is employed within stacked-ensemble to capture higher-order relationships among model outputs. Experiments conducted on the Lending Club dataset demonstrate that the proposed framework improves predictive performance compared with individual classifiers. The BlendNet ensemble achieved the strongest results with an AUC of 0.80, a macro-average F1-score of 0.73, and a default recall of 0.81. Calibration analysis further shows that tree-based ensembles such as Extra Trees and Gradient Boosting provide the most reliable probability estimates, while the stacked ensemble offers superior ranking capability. Feature analysis using Recursive Feature Elimination identifies revolving utilisation, annual income, and debt-to-income ratio as the most influential predictors of loan default. These findings demonstrate that performance-driven ensemble weighting can improve both predictive accuracy and interpretability in credit risk modelling. The proposed framework provides a scalable data-driven approach to support institutional credit assessment, risk monitoring, and financial decision-making.

Credit risk scoring must support high-stakes lending decisions where data distributions change over time, probability estimates must be reliable, and group-level fairness is required. While modern machine learning models improve default prediction accuracy, they often produce poorly calibrated scores under distribution shift and may create unfair outcomes when trained without explicit constraints. This paper proposes Calibrated Credit Intelligence (CCI), a deployment-oriented framework that combines (i) a Bayesian neural risk scorer to capture epistemic uncertainty and reduce overconfident errors, (ii) a fairnessconstrained gradient boosting model to control group disparities while preserving strong tabular performance, and (iii) a shiftaware fusion strategy followed by post-hoc probability calibration to stabilize decision thresholds in later time periods. We evaluate CCI on the Home Credit Credit Risk Model Stability benchmark using a time-consistent split to reflect real-world drift. Compared with strong baselines (LightGBM, XGBoost, CatBoost, TabNet, and a standalone Bayesian neural model), CCI achieves the best overall trade-off between discrimination, calibration, stability, and fairness. In particular, CCI reaches an AUC-ROC of 0.912 and an AUC-PR of 0.438, improves operational performance with Recall@1%FPR = 0.509, and reduces calibration error (Brier score 0.087, ECE 0.015). Under temporal shift, CCI shows a smaller AUC-PR drop from early to late periods (0.017), and it lowers group disparities (demographic parity gap 0.046, equal opportunity gap 0.037) compared to unconstrained boosting. These results indicate that CCI produces risk scores that are accurate, reliable, and more equitable under realistic deployment conditions.

Organizations often have an incumbent predictive model in production when new data sources become available. Because historical training data lack the new features, a challenger model must be trained on a small but growing full-feature dataset. We study whether, and when, the organization should switch to the challenger. The decision is statistical and economic: the challenger's predictive performance improves as full-feature data accumulate, but repeated retraining is costly and delays benefits from deployment. We develop a framework linking learning-curve dynamics to model-switching economics. Under a standard power-law learning curve and finite data-collection horizon $T$, the optimal time to train and evaluate the challenger scales as $T^{1/(1+α)}$: learning-curve shape (through its learning speed $α$) is the primary theoretical determinant of when to stop experimenting; costs determine switching profitability. Even without knowing the learning curve, the operational problem is tractable: we show that any algorithm stopping on the $T^{2/3}$ scale and making reliable switch/discard decisions achieves $O(T^{2/3}\sqrt{\log T})$ regret relative to a full-foresight oracle. We propose a sequential evaluation algorithm that uses local learning-curve trends to anticipate improvement, and test it in a real-world credit-scoring study. Even with this local approximation, the algorithm theoretically and empirically achieves near-oracle performance. It is also more stable than greedy sequential evaluation algorithms, where noisy early estimates trigger premature discarding, or simple one-shot evaluation algorithms, which work only when their fixed evaluation time matches the (unknown in practice) theoretical timing scale. Our framework offers a step toward principled model governance when new data sources require costly collection, validation, and deployment.

Traditional decision tree models, which rely exclusively on numerical variables, often face challenges in handling high-dimensional data and are limited in their ability to incorporate textual information effectively. To address these limitations, we propose the integrated multivariate segmentation tree (IMST), a comprehensive framework designed to improve credit evaluation for small- and medium-sized enterprises (SMEs) by integrating financial data with textual sources. This method comprises three core stages: (1) transforming textual data into numerical matrices through matrix factorization, (2) selecting salient financial features using Lasso regression, and (3) constructing a multivariate segmentation tree based on either the Gini index or entropy, with weakest-link pruning applied to control model complexity. Experimental results based on a dataset of 1,428 Chinese SMEs demonstrated that IMST achieved an accuracy rate of 88.9%, surpassing both baseline decision trees (87.4%) and conventional models such as support vector machines and neural networks. Furthermore, the proposed model demonstrated superior interpretability and computational efficiency, featuring a more streamlined architecture and improved risk detection capabilities.

Recent advancements in financial problem-solving have leveraged LLMs and agent-based systems, with a primary focus on trading and financial modeling. However, credit assessment remains an underexplored challenge, traditionally dependent on rule-based methods and statistical models. In this paper, we introduce MASCA, an LLM-driven multi-agent system designed to enhance credit evaluation by mirroring real-world decision-making processes. The framework employs a layered architecture where specialized LLM-based agents collaboratively tackle sub-tasks. Additionally, we integrate contrastive learning for risk and reward assessment to optimize decision-making. We further present a signaling game theory perspective on hierarchical multi-agent systems, offering theoretical insights into their structure and interactions. Our paper also includes a detailed bias analysis in credit assessment, addressing fairness concerns. Experimental results demonstrate that MASCA outperforms baseline approaches, highlighting the effectiveness of hierarchical LLM-based multi-agent systems in financial applications, particularly in credit scoring.

Fairness in decision-making processes is often quantified using probabilistic metrics. However, these metrics need not reflect the consequences of decisions for the affected individuals and groups. We develop a utility-based framework that incorporates these consequences into the assessment of fairness. Our main result shows that a decision-making process can satisfy $\varepsilon$-fairness while nevertheless being maximally unfair once the utilities associated with its outcomes are taken into account. To address applications in which information on false negatives is unavailable, we also formulate a reduced setting that retains the essential elements of the utility-based fairness assessment. We illustrate the framework through two applications: college admissions and credit-risk assessment. In both cases, probabilistic metrics may classify a decision-making process as approximately fair even though the corresponding utility outcomes are highly unequal. In the college-admissions example, our analysis shows that improving completion rates is necessary to achieve equality of utility across groups, while in the mortgage example, mitigating unfairness requires not only adjusting approval rates but also reducing the adverse consequences of default. These findings demonstrate that fairness assessments should account not only for the probabilities of different decisions but also for the consequences of those decisions.

Credit scoring has been catalogued by the European Commission and the Executive Office of the US President as a high-risk classification task, in light of the potential harms of making loan approval decisions based on models that would be biased against certain groups. To address this concern, recent credit scoring research has considered a range of fairness-enhancing techniques put forward by the machine learning community to reduce bias and unfair treatment in classification systems. While the definition of fairness or the approach they follow to impose it may vary, most of these techniques, however, disregard the robustness of the results. This can create situations where unfair treatment is effectively corrected in the training set, but when producing out-of-distribution classifications, unfair treatment is incurred again. Instead, in this paper, we will investigate how to apply Distributionally Robust Optimisation (DRO) methods to credit scoring, thereby empirically evaluating how they perform in terms of fairness, ability to classify correctly, and the robustness of the solution against changes in the marginal proportions. In so doing, we find DRO methods to provide a substantial improvement in terms of fairness, with almost no loss in predictive performance. These results thus indicate that DRO can improve fairness in credit scoring, provided that further advances are made in efficiently implementing these systems. In addition, our analysis suggests that many of the commonly used fairness metrics are not ideally suited to the credit scoring setting, as they evaluate performance at a single classification threshold.