# Neural networks-based algorithms for stochastic control and PDEs in finance

arXiv: https://arxiv.org/abs/2101.08068 · HTML: https://mlsanity.com/paper/2101.08068/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2021.

## Built on by (most cited first, 26 of 26)

- [Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality](https://mlsanity.com/paper/2106.08900/) (2021)
- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Mean-field neural networks: learning mappings on Wasserstein space](https://mlsanity.com/paper/2210.15179/) (2022)
- [Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates](https://mlsanity.com/paper/2407.08100/) (2024)
- [Mean-field neural networks-based algorithms for McKean-Vlasov control problems *](https://mlsanity.com/paper/2212.11518/) (2022)
- [Deep neural network expressivity for optimal stopping problems](https://mlsanity.com/paper/2210.10443/) (2022)
- [Neural Q-learning for solving PDEs](https://mlsanity.com/paper/2203.17128/) (2022)
- [An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning](https://mlsanity.com/paper/2408.13222/) (2024)
- [Temporal Difference Learning with Continuous Time and State in the Stochastic Setting](https://mlsanity.com/paper/2202.07960/) (2022)
- [A brief review of the Deep BSDE method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2505.17032/) (2025)
- [One model to solve them all: 2BSDE families via neural operators](https://mlsanity.com/paper/2511.01125/) (2025)
- [Simultaneous upper and lower bounds of American-style option prices with hedging via neural networks](https://mlsanity.com/paper/2302.12439/) (2023)
- [Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks](https://mlsanity.com/paper/2407.02827/) (2024)
- [P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization](https://mlsanity.com/paper/2410.03801/) (2024)
- [An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Control](https://mlsanity.com/paper/2410.05163/) (2024)
- [On Parametric Optimal Execution and Machine Learning Surrogates](https://mlsanity.com/paper/2204.08581/) (2022)
- [Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study](https://mlsanity.com/paper/2311.07231/) (2023)
- [Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations](https://mlsanity.com/paper/2302.03286/) (2023)
- [Deep Learning for Mean Field Optimal Transport](https://mlsanity.com/paper/2302.14739/) (2023)
- [Quantile and moment neural networks for learning functionals of distributions](https://mlsanity.com/paper/2303.11060/) (2023)
- [Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness](https://mlsanity.com/paper/2307.02454/) (2023)
- [PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learning](https://mlsanity.com/paper/2505.22085/) (2025)
- [Error analysis for the deep Kolmogorov method](https://mlsanity.com/paper/2508.17167/) (2025)
- [Random Neural Network Expressivity for Non-Linear Partial Differential Equations](https://mlsanity.com/paper/2605.25057/) (2026)
- [Deep numerical schemes for systems of Ergodic BSDEs with applications to regime-switching forward utilities](https://mlsanity.com/paper/2606.24271/) (2026)

## Abstract (arXiv)

This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and derivative pricing in financial engineering. We survey recent results in the literature, present new developments, notably in the fully nonlinear case, and compare the different schemes illustrated by numerical tests on various financial applications. We conclude by highlighting some future research directions.