# Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation

arXiv: https://arxiv.org/abs/2511.08606 · HTML: https://mlsanity.com/paper/2511.08606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2025.

## Abstract (arXiv)

In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability measure to recover the backward stochastic differential equation (BSDE) from a single pair of stock and option trajectories. Unlike existing approaches to identifying stochastic differential equations-which typically require ergodicity-our framework leverages the risk-neutral measure, thereby eliminating the ergodicity assumption and enabling BSDE recovery from limited financial time series data. Using this algorithm, we are able not only to make forward-looking predictions but also to generate new synthetic data paths consistent with the underlying probabilistic law.