← 研踪 PaperTrailarXiv:2511.07235 · v2
Deep Neural Operator Learning for Probabilistic Models
首次提交 2025-11-10 23:52
版本更新 2026-11-05 19:21
雷达观测 2026-11-06 12:09
摘要
We propose a deep neural-operator framework for a general class of probabilistic 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.
作者备注：typos corrected
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v2 · 2026-11-05 19:21 · 最新观测版本
Deep Neural Operator Learning for Probabilistic Models
We propose a deep neural-operator framework for a general class of probabilistic 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.
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