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

Qi Feng; Guang Lin; Purav Matlia; Denny Serdarevic

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arXiv · 2511.08606

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

Qi Feng·Guang Lin·Purav Matlia·Denny Serdarevic

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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.

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BibTeX RIS

Qi Feng, Guang Lin, Purav Matlia, Denny Serdarevic. 2025-11-05. Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation. https://arxiv.org/abs/2511.08606

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