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

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  • Qi Feng
  • Guang Lin
  • Purav Matlia
  • Denny Serdarevic

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.

Suggested Citation

  • Qi Feng & Guang Lin & Purav Matlia & Denny Serdarevic, 2025. "Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation," Papers 2511.08606, arXiv.org.
    • Handle: RePEc:arx:papers:2511.08606
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    References listed on IDEAS

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    1. Zhao Chen & Yang Liu & Hao Sun, 2021. "Physics-informed learning of governing equations from scarce data," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    2. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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