Work

Convergence Analysis of Iterative Deep Learning Algorithms for Fully Nonlinear BSPDEs in Non-Markovian Utility Maximization

Year: 2026

Type: 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.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-026-03416-3

Authors: Jingtang Ma, Haofei Wu, H. Harry Zheng

Institutions: Southwestern University of Finance and Economics, Hong Kong Polytechnic University, Academy of Mathematics and Systems Science, Imperial College London

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Natural Science Foundation of China, Southwestern University of Finance and Economics, Engineering and Physical Sciences Research Council