Deep Neural Operator Learning for Probabilistic Models

Erhan Bayraktar; Qi Feng; Zecheng Zhang; Zhaoyu Zhang

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arXiv · 2511.07235

Deep Neural Operator Learning for Probabilistic Models

Erhan Bayraktar·Qi Feng·Zecheng Zhang·Zhaoyu Zhang

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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.

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Erhan Bayraktar, Qi Feng, Zecheng Zhang, Zhaoyu Zhang. 2025-11-10. Deep Neural Operator Learning for Probabilistic Models. https://arxiv.org/abs/2511.07235

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