Convergence analysis of iterative deep learning algorithms for fully nonlinear BSPDEs in non-Markovian utility maximization
File(s)
Published version
Author(s)
Ma, Jingtang
Wu, Haofei
Zheng, Harry
Type
Journal Article
Abstract
In utility maximization with non-Markovian setting, the value function satisfies a stochastic Hamilton-Jacobi-Bellman (HJB) equation, a fully nonlinear backward stochastic partial differential equation (BSPDE). We propose iterative deep learning algorithms for such BSPDEs and analyze their convergence. We derive the error estimate of the time discretization scheme for BSPDEs, that of the policy iteration scheme for discretized BSPDEs, and that of the iterative deep learning scheme for discretized BSPDEs. We also test the algorithms and show their convergence and accuracy with numerical examples, including Markovian Heston volatility model and non-Markovian rough volatility model.
Date Issued
2026-09-01
Date Acceptance
2026-07-16
Citation
Journal of Scientific Computing, 2026, 108 (3)
ISSN
0885-7474
Publisher
Springer
Journal / Book Title
Journal of Scientific Computing
Volume
108
Issue
3
Copyright Statement
© 2026 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s10915-026-03416-3
Subjects
Utility maximization
Non-Markovian model
Fully nonlinear BSPDE
Policy iteration
Deep learning
Error estimate
Convergence analysis Mathematics Subject Classification 60H35
65C30
93E20 B H. Harry Zheng
Publication Status
Published
Article Number
95
Date Publish Online
2026-07-28