arXiv subjects

Alexandre Alouadi

Publications and source records attributed to Alexandre Alouadi.

7 recordsLinked to original sources

arXiv2026

Deep-MKV-TS: Path-Dependent McKean--Vlasov Control for Financial Time Series Generation

We introduce Deep-MKV-TS, a path-dependent McKean-Vlasov framework for financial scenario generation. The stochastic dynamics are chosen by matching selected path and volatility features of generated scenarios to those observed in the data. Starting from an interpretable reference model, Deep-MKV-TS preserves the reference drift and adjusts its volatility, while a regularization penalty limits unnecessary departures from the calibrated dynamics. We solve the resulting control problem using a neural, sample-based implementation of the stochastic maximum principle. We validate the method against an exactly computable oracle. On Heston and Heston-mixture models, Deep-MKV-TS substantially reduces path-dependent and volatility-related deficiencies of the reference model. In delayed-volatility experiments, the correction remains effective as the forecasting horizon increases, while direct training becomes less reliable. On held-out intraday equity-index futures, the corrected model improves conditional forecasts relative to the reference and reaches a level of performance comparable to flexible generative and historical baselines. The resulting scenarios also support greater exposure than the reference under a fixed drawdown-risk target. These results show that path-dependent McKean-Vlasov control can enrich an interpretable reference model without replacing it.

q-fin.CP↗

arXiv2026

The Fundamental Structure of Risk: From Characteristics to Covariance

Estimating the covariance structure of financial assets typically relies on historical returns, making risk models dependent on noisy and asset-specific time series. We propose the Characteristic-Driven Dynamic Factor Model (CD-DFM), a non-linear latent factor model that instead constructs a representation of the asset cross-section directly from observable firm characteristics, primarily company fundamentals. The learned latent space jointly determines interpretable factor exposures and a forward covariance estimator, and is trained end to end on an objective that combines a Stein covariance loss with a factor reconstruction term, targeting the out-of-sample second moments used in risk management. Because the latent representation, i.e. the encoder depends only on characteristics, previously unseen assets can be embedded at inference time without retraining. Experiments on S&P 500 equities show that CD-DFM produces economically structured latent representations, interpretable factor portfolios, and competitive covariance forecasts despite relying on substantially lower-frequency information than return-based approaches. Among the benchmarked methods, it is the only model that simultaneously combines characteristic-driven representations, factor interpretability, competitive covariance calibration, and zero-shot onboarding of unseen assets.

q-fin.ST↗

arXiv2026

Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approach

We propose a generative framework for learning stochastic dynamics from endpoint and intermediate distributional observations. The method formulates generation as a McKean-Vlasov control problem in which terminal and time-marginal laws are enforced through soft energy constraints. The associated optimality system is a forward-backward stochastic differential equation (FBSDE) whose backward component receives a continuous drift induced by the marginal law penalties. This provides a principled alternative to hard interpolation or optimal transport maps between observed distributions: the model learns a stochastic path law whose dynamics remain globally coupled through the mean-field objective. We derive the reduced FBSDE system for quadratic control cost and constant diffusion, connecting terminal and marginal law flat derivatives to score-like training signals. The resulting neural solver is evaluated on low-dimensional distributional benchmarks, where it recovers smooth stochastic paths matching prescribed marginal laws. In a higher-dimensional ALAE latent space, endpoint supervision is used as a qualitative stress test for transporting non-smiling faces toward smiling ones in a pretrained representation. We then use articulated human motion as a structured high-dimensional case study on a curated AMASS low-to-high position dataset, using SMPL-H pose sequences and reduced pose representations. The experiments show that soft marginal law constraints can produce coherent stochastic trajectories whose intermediate distributions follow the observed evolution of human motion. The code is available at https://github.com/murex/deep-mkv-gen/tree/main.

math.OC↗

arXiv2026

SBBTS: A Unified Schr\"odinger-Bass Framework for Synthetic Financial Time Series

We study the problem of generating synthetic time series that reproduce both marginal distributions and temporal dynamics, a central challenge in financial machine learning. Existing approaches typically fail to jointly model drift and stochastic volatility, as diffusion-based methods fix the volatility while martingale transport models ignore drift. We introduce the Schr\"odinger-Bass Bridge for Time Series (SBBTS), a unified framework that extends the Schr\"odinger-Bass formulation to multi-step time series. The method constructs a diffusion process that jointly calibrates drift and volatility and admits a tractable decomposition into conditional transport problems, enabling efficient learning. Numerical experiments on the Heston model demonstrate that SBBTS accurately recovers stochastic volatility and correlation parameters that prior Schr\"odingerBridge methods fail to capture. Applied to S&P 500 data, SBBTS-generated synthetic time series consistently improve downstream forecasting performance when used for data augmentation, yielding higher classification accuracy and Sharpe ratio compared to real-data-only training. These results show that SBBTS provides a practical and effective framework for realistic time series generation and data augmentation in financial applications.

cs.LG↗

arXiv2026

LightSBB-M: Bridging Schr\"odinger and Bass for Generative Diffusion Modeling

The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that computes the optimal SBB transport plan in only a few iterations. The method exploits a dual representation of the SBB objective to obtain analytic expressions for the optimal drift and volatility, and it incorporates a tunable parameter beta greater than zero that interpolates between pure drift (the Schrodinger Bridge) and pure volatility (Bass martingale transport). We show that LightSBB-M achieves the lowest 2-Wasserstein distance on synthetic datasets against state-of-the-art SB and diffusion baselines with up to 32 percent improvement. We also illustrate the generative capability of the framework on an unpaired image-to-image translation task (adult to child faces in FFHQ). These findings demonstrate that LightSBB-M provides a scalable, high-fidelity SBB solver that outperforms existing SB and diffusion baselines across both synthetic and real-world generative tasks. The code is available at https://github.com/alexouadi/LightSBB-M.

cs.LG↗

arXiv2026

A PDE Derivation of the Schr\"odinger--Bass Bridge

This short paper announces the main results of \cite{SBB2026}, where the Schr\"odinger--Bass Bridge (SBB) problem is introduced and studied in full generality. Here we provide a direct PDE derivation of the SBB system in dimension one, showing how the optimal coupling problem that interpolates between the classical Schr\"odinger bridge and the Bass martingale transport can be solved explicitly via Legendre transforms and the heat equation. A key insight is that the optimal SBB process is a Stretched Schr\"odinger Bridge: the composition of a monotone transport map with a Schr\"odinger bridge. This extends the stretched Brownian motion representation of Bass martingales to the semimartingale setting and provides a unified framework that recovers both the Sinkhorn algorithm (in the limit $\beta \to \infty$) and the Bass construction (as $\beta \to 0$). We refer to \cite{SBB2026} for complete proofs, the multidimensional setting, strong duality, dual attainment, and further developments.

math.PR↗

arXiv2025

Robust time series generation via Schr\"odinger Bridge: a comprehensive evaluation

We investigate the generative capabilities of the Schr\"odinger Bridge (SB) approach for time series. The SB framework formulates time series synthesis as an entropic optimal interpolation transport problem between a reference probability measure on path space and a target joint distribution. This results in a stochastic differential equation over a finite horizon that accurately captures the temporal dynamics of the target time series. While the SB approach has been largely explored in fields like image generation, there is a scarcity of studies for its application to time series. In this work, we bridge this gap by conducting a comprehensive evaluation of the SB method's robustness and generative performance. We benchmark it against state-of-the-art (SOTA) time series generation methods across diverse datasets, assessing its strengths, limitations, and capacity to model complex temporal dependencies. Our results offer valuable insights into the SB framework's potential as a versatile and robust tool for time series generation.

cs.LG↗