Deep Learning for High-Dimensional Continuous-Time Stochastic Optimal Control Without Explicit Solution

Jean-Loup Dupret and Donatien Hainaut
Additional contact information
Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2026035, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This paper introduces the generalized policy iteration physics-informed neural network algorithm, a novel numerical scheme for solving continuous-time stochastic optimal control problems in high dimensions when the optimal control does not admit an explicit solution. The proposed iterative deep learning algorithm leverages physics-informed neural networks on the Hamilton–Jacobi–Bellman residuals in an actor-critic fashion, which is built from the generalized policy iteration technique. It employs two separate neural networks to approximate both the value function and the multidimensional optimal control, achieving a global approximation of the optimal solution across all time and space that can be evaluated online rapidly. Theoretical guarantees on convergence and optimality are provided, whereas its accuracy and efficacy are empirically validated through two important numerical examples from operations research. In particular, we generalize the standard Almgren–Chriss model arising from optimal liquidation in finance by allowing for a price impact model with fully nonlinear temporary and permanent impact functions and by considering a multidimensional setting with numerous cointegrated assets.

Keywords: Financial Engineering; stochastic optimal control; deep learning; physics-informed neural networks; optimal liquidation; partial differential equation (search for similar items in EconPapers)
Pages: 22
Date: 2026-02-05
Note: In: Operations Research, 2026, vol. 74(3), p. 1241-1262
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2026035

DOI: 10.1287/opre.2024.1102

Access Statistics for this paper

More papers in LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA) Voie du Roman Pays 20, 1348 Louvain-la-Neuve (Belgium). Contact information at EDIRC.
Bibliographic data for series maintained by Alain Gillis ().