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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08606 |
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| _version_ | 1866909898580688896 |
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| author | Feng, Qi Lin, Guang Matlia, Purav Serdarevic, Denny |
| author_facet | Feng, Qi Lin, Guang Matlia, Purav Serdarevic, Denny |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation Feng, Qi Lin, Guang Matlia, Purav Serdarevic, Denny Mathematical Finance Artificial Intelligence Computational Finance 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. |
| title | Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation |
| topic | Mathematical Finance Artificial Intelligence Computational Finance |
| url | https://arxiv.org/abs/2511.08606 |