Fraud detection models in payment networks train on chargeback labels that are systematically biased. Every label must survive three sequential gates: authorization (declined transactions generate no labels), issuer reporting (unreported fraud is invisible), and delay (pending chargebacks are missing at training time). Labels that do arrive may be corrupted by first-party misuse or issuer misclassification. A companion paper [arXiv:2605.27557] proved that these four impairments impose a minimax lower bound on detection performance. This paper asks: can that bound be achieved? We formalize the observation pipeline as a sequential missing-data problem with three propensity stages and a corruption layer, and construct the Sequential Triply Robust (STR) estimator. The STR corrects for all four impairments simultaneously and achieves the semiparametric efficiency bound -- no estimator can have lower asymptotic variance. It is sequentially triply robust: at each gate, consistency requires only that either the propensity model or the outcome regression is correctly specified, not both. We provide corruption correction via noise-rate-adjusted pseudo-labels, empirical Bayes shrinkage to stabilize inverse-propensity weights for small issuers, a plug-in variance estimator yielding valid confidence intervals, and a Bernstein concentration inequality for finite-sample guarantees. On the operational side, we derive the optimal training delay -- the maturity window that minimizes the sum of label-quality loss and model staleness -- and prove that the STR permits training on data that is days old rather than months old, decoupling model freshness from the chargeback maturity cycle. The STR provably dominates naive chargeback-based training in mean squared error for any sample size.

This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling. We demonstrate that standard generative models and unconstrained statistical extrapolations suffer from "manifold collapse" and severe arbitrage violations when forecasting term structures across diverse macroeconomic regimes. To overcome this, we propose a two-stage architecture. First, a Student-t Conditional Variational Autoencoder with Dynamic Level Injection (CVAEsT+LS) extracts a robust, heavy-tailed term structure manifold, effectively decoupling macroeconomic shape dynamics from absolute base rates. Second, the latent dynamic evolution is governed by a continuous-time Neural Stochastic Differential Equation (SDE) strictly penalized by a No-Arbitrage Partial Differential Equation (PDE). Empirical results across multiple sovereign currencies (USD, GBP, JPY) confirm that our synergistic approach drastically reduces out-of-sample forecasting errors -- achieving an exceptional 6.58 bps Mean Tenor RMSE -- and successfully overcomes the massive parallel drift and zero-lower-bound violations exhibited by the classical HJM model in extreme environments. Furthermore, through phase space vector field analysis, we demonstrate the model's superior capability in unsupervised macroeconomic regime detection and high-quality continuous-time scenario generation. Ultimately, this research provides a highly scalable, mathematically sound evolutionary engine for term structure modeling.

This paper proposes a hybrid methodology to improve the approximation of SABR (Stochastic Alpha Beta Rho) implied volatility by combining analytical structure with machine learning. The approach augments the neural-network input representation with geometric features derived from the stochastic differential equations of the SABR model. Unlike approaches that fully replace analytical formulas with black-box models, the proposed framework preserves the analytical backbone of the model. The hybridization operates along two complementary dimensions. First, geometry-aware variables reflecting intrinsic properties of the SABR dynamics are used as structured inputs to the network. Second, the neural network is trained to learn the residual error relative to Hagan's closed-form approximation rather than implied volatility directly. The resulting model acts as a structured residual correction to the analytical formula, retaining interpretability while capturing higher-order effects that are not included in the asymptotic expansion. Numerical experiments conducted over realistic parameter domains, as well as stressed environments, show that the method improves accuracy and robustness compared with both analytical approximations and standard neural-network approaches. Because the correction remains lightweight and structurally consistent with the underlying model, the framework is well suited for real-time pricing and calibration in practical trading environments.

Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally modeled by stochastic differential equations (SDEs), whose forward and reverse density evolution closely parallels the forward noising and reverse denoising structure of diffusion models. In this paper, we develop a framework for using DDPMs to generate risk-neutral asset price dynamics for derivative valuation. Starting from log-return dynamics under the physical measure, we analyze the associated forward diffusion and derive the reverse-time SDE. We show that the change of measure from the physical to the risk-neutral measure induces an additive shift in the score function, which translates into a closed-form risk-neutral epsilon shift in the DDPM reverse dynamics. This correction enforces the risk-neutral drift while preserving the learned variance and higher-order structure, yielding an explicit bridge between diffusion-based generative modeling and classical risk-neutral SDE-based pricing. We show that the resulting discounted price paths satisfy the martingale condition under the risk-neutral measure. Empirically, the method reproduces the risk-neutral terminal distribution and accurately prices both European and path-dependent derivatives, including arithmetic Asian options, under a GBM benchmark. These results demonstrate that diffusion-based generative models provide a flexible and principled approach to simulation-based derivative pricing.

We study U.S. Treasury yield curve forecasting under distributional uncertainty and recast forecasting as an operations research and managerial decision problem. Rather than minimizing average forecast error, the forecaster selects a decision rule that minimizes worst case expected loss over an ambiguity set of forecast error distributions. To this end, we propose a distributionally robust ensemble forecasting framework that integrates parametric factor models with high dimensional nonparametric machine learning models through adaptive forecast combinations. The framework consists of three machine learning components. First, a rolling window Factor Augmented Dynamic Nelson Siegel model captures level, slope, and curvature dynamics using principal components extracted from economic indicators. Second, Random Forest models capture nonlinear interactions among macro financial drivers and lagged Treasury yields. Third, distributionally robust forecast combination schemes aggregate heterogeneous forecasts under moment uncertainty, penalizing downside tail risk via expected shortfall and stabilizing second moment estimation through ridge regularized covariance matrices. The severity of the worst case criterion is adjustable, allowing the forecaster to regulate the trade off between robustness and statistical efficiency. Using monthly data, we evaluate out of sample forecasts across maturities and horizons from one to twelve months ahead. Adaptive combinations deliver superior performance at short horizons, while Random Forest forecasts dominate at longer horizons. Extensions to global sovereign bond yields confirm the stability and generalizability of the proposed framework.

We develop an arbitrage-free deep learning framework for yield curve and bond price forecasting based on the Heath-Jarrow-Morton (HJM) term-structure model and a dynamic Nelson-Siegel parameterization of forward rates. Our approach embeds a no-arbitrage drift restriction into a neural state-space architecture by combining Kalman, extended Kalman, and particle filters with recurrent neural networks (LSTM/CLSTM), and introduces an explicit arbitrage error regularization (AER) term during training. The model is applied to U.S. Treasury and corporate bond data, and its performance is evaluated for both yield-space and price-space predictions at 1-day and 5-day horizons. Empirically, arbitrage regularization leads to its strongest improvements at short maturities, particularly in 5-day-ahead forecasts, increasing market-consistency as measured by bid-ask hit rates and reducing dollar-denominated prediction errors.

We propose ARBITER, a risk-neutral neural operator for learning joint SPX-VIX term structures under no-arbitrage constraints. ARBITER maps market states to an operator that outputs implied volatility and variance curves while enforcing static arbitrage (calendar, vertical, butterfly), Lipschitz bounds, and monotonicity. The model couples operator learning with constrained decoders and is trained with extragradient-style updates plus projection. We introduce evaluation metrics for derivatives term structures (NAS, CNAS, NI, Dual-Gap, Stability Rate) and show gains over Fourier Neural Operator, DeepONet, and state-space sequence models on historical SPX and VIX data. Ablation studies indicate that tying the SPX and VIX legs reduces Dual-Gap and improves NI, Lipschitz projection stabilizes calibration, and selective state updates improve long-horizon generalization. We provide identifiability and approximation results and describe practical recipes for arbitrage-free interpolation and extrapolation across maturities and strikes.

Robust yield curve estimation is crucial in fixed-income markets for accurate instrument pricing, effective risk management, and informed trading strategies. Traditional approaches, including the bootstrapping method and parametric Nelson-Siegel models, often struggle with overfitting or instability issues, especially when underlying bonds are sparse, bond prices are volatile, or contain hard-to-remove noise. In this paper, we propose a neural networkbased framework for robust yield curve estimation tailored to small mortgage bond markets. Our model estimates the yield curve independently for each day and introduces a new loss function to enforce smoothness and stability, addressing challenges associated with limited and noisy data. Empirical results on Swedish mortgage bonds demonstrate that our approach delivers more robust and stable yield curve estimates compared to existing methods such as Nelson-Siegel-Svensson (NSS) and Kernel-Ridge (KR). Furthermore, the framework allows for the integration of domain-specific constraints, such as alignment with risk-free benchmarks, enabling practitioners to balance the trade-off between smoothness and accuracy according to their needs.