Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation
This work addresses the challenge of identifying stochastic differential equations in finance without requiring ergodicity, which is incremental as it builds on existing SINDy methods but applies them under a risk-neutral measure.
The paper tackled the problem of discovering probabilistic laws underlying the Feynman-Kac formula by introducing a data-driven framework that recovers backward stochastic differential equations from limited financial data, enabling both prediction and synthetic data generation.
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.