{"ID":2844039,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.07235","arxiv_id":"2511.07235","title":"Deep Neural Operator Learning for Probabilistic Models","abstract":"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.","short_abstract":"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 archite...","url_abs":"https://arxiv.org/abs/2511.07235","url_pdf":"https://arxiv.org/pdf/2511.07235v1","authors":"[\"Erhan Bayraktar\",\"Qi Feng\",\"Zecheng Zhang\",\"Zhaoyu Zhang\"]","published":"2025-11-10T15:52:48Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"q-fin.CP\"]","methods":"[]","has_code":false}