Paper: arXiv 2602.20011

Authors: Stefano De Marco, Huyên Pham, Davide Zanni

Abstract

We study generative modeling for time series using entropic optimal transport and the Schrödinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche, Henry-Labordère, Pham, 2023, we introduce a jump-diffusion Schrödinger bridge model that allows for discontinuities in the generative dynamics. Starting from a Schrödinger bridge entropy minimization problem, we reformulate the task as a stochastic control problem whose solution characterizes the optimal controlled jump-diffusion process. When sampled on a fixed time grid, this process generates synthetic time series matching the joint distributions of the observed data. The model is fully data-driven, as both the drift and the jump intensity are learned directly from the data. We propose practical algorithms for training, sampling, and hyperparameter calibration. Numerical experiments on simulated and real datasets, including financial and energy time series, show that incorporating jumps substantially improves the realism of the generated data, in particular by capturing abrupt movements, heavy tails, and regime changes that diffusion-only models fail to reproduce. Comparisons with state-of-the-art generative models highlight the benefits and limitations of the proposed approach.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical extension of Schrödinger bridges to càdlàg jump-diffusion processes via stochastic control theory. It complements the strong theoretical derivations with practical calibration algorithms and empirical testing on real financial and energy time series to demonstrate superior handling of heavy tails and regime changes.

Research Flowchart

  flowchart TD
    A[Research Goal: Realistic Generative Time Series Modeling for Financial & Energy Data] --> B[Data Inputs: Simulated & Real Time Series Data]
    B --> C[Methodology: Jump-Diffusion Schrödinger Bridge Framework]
    C --> D[Stochastic Control Reformulation: Entropy Minimization to Optimal Control]
    D --> E[Data-Driven Model Training: Learn Drift & Jump Intensity]
    E --> F[Grid Sampling: Generate Synthetic Time Series]
    F --> G[Outcomes: Improved Realism Capturing Heavy Tails, Abrupt Jumps & Regime Changes]

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1 of 42 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.