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Deep Neural Operator Learning for Probabilistic Models

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2511.07235

Authors: Bayraktar, Erhan, Feng, Qi, Zhang, Zecheng, Zhang, Zhaoyu

Institutions: University of Michigan, Florida State University, University of Notre Dame, University of California, Los Angeles

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Wasserstein PDEs and Applications to Optimization and Learning, Hypoelliptic and Non-Markovian stochastic dynamical systems in machine learning and mathematical finance: from theory to application

OpenAlex ID: W7105099652

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