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

• URL: http://arxiv.org/abs/2511.08606v1
• Date: Thu, 13 Nov 2025 01:00:32 GMT
• Title: Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation
• Authors: Qi Feng, Guang Lin, Purav Matlia, Denny Serdarevic,
• Abstract summary: We introduce the first SINDy method formulated under the risk-neutral probability measure to recover the backward differential equation (BSDE) from a single pair of stock and option trajectories.<n>We are able not only to make forward-looking predictions but also to generate new synthetic data paths consistent with the underlying probabilistic law.
• Score: 9.24445668058824
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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