{"ID":2845597,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08606","arxiv_id":"2511.08606","title":"Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation","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.","short_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...","url_abs":"https://arxiv.org/abs/2511.08606","url_pdf":"https://arxiv.org/pdf/2511.08606v1","authors":"[\"Qi Feng\",\"Guang Lin\",\"Purav Matlia\",\"Denny Serdarevic\"]","published":"2025-11-05T01:57:01Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"cs.AI\",\"q-fin.CP\"]","methods":"[]","has_code":false}