Deep Neural Operator Learning for Probabilistic Models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909896482488320 |
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| author | Bayraktar, Erhan Feng, Qi Zhang, Zecheng Zhang, Zhaoyu |
| author_facet | Bayraktar, Erhan Feng, Qi Zhang, Zecheng Zhang, Zhaoyu |
| contents | We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal approximation theorem with explicit network-size bounds for the proposed architecture. The underlying stochastic processes are required only to satisfy integrability and general tail-probability conditions. We verify these assumptions for both European and American option-pricing problems within the forward-backward SDE (FBSDE) framework, which in turn covers a broad class of operators arising from parabolic PDEs, with or without free boundaries. Finally, we present a numerical example for a basket of American options, demonstrating that the learned model produces optimal stopping boundaries for new strike prices without retraining. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Neural Operator Learning for Probabilistic Models Bayraktar, Erhan Feng, Qi Zhang, Zecheng Zhang, Zhaoyu Machine Learning Computational Finance We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal approximation theorem with explicit network-size bounds for the proposed architecture. The underlying stochastic processes are required only to satisfy integrability and general tail-probability conditions. We verify these assumptions for both European and American option-pricing problems within the forward-backward SDE (FBSDE) framework, which in turn covers a broad class of operators arising from parabolic PDEs, with or without free boundaries. Finally, we present a numerical example for a basket of American options, demonstrating that the learned model produces optimal stopping boundaries for new strike prices without retraining. |
| title | Deep Neural Operator Learning for Probabilistic Models |
| topic | Machine Learning Computational Finance |
| url | https://arxiv.org/abs/2511.07235 |