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

Qi Feng, Guang Lin, Purav Matlia and Denny Serdarevic

Papers from arXiv.org

Abstract: 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.

Date: 2025-11
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Published in 39th Conference on Neural Information Processing Systems (NeurIPS 2025) Workshop: Generative AI in Finance

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