mlsanityData to 7 Oct 2026

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

arXiv 2101.08068 ↗First posted 20 Jan 2021math.OC q-fin.CPcited by 26

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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.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Jan 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 6; 2023: 7; 2024: 5; 2025: 4; 2026: 2.

26 papers.

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  1. 2021Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionalitycited by 34
  2. 2021Deep Learning for Mean Field Games and Mean Field Control with Applications to Financecited by 20
  3. 2023Recent Developments in Machine Learning Methods for Stochastic Control and Gamescited by 19
  4. 2022Mean-field neural networks: learning mappings on Wasserstein spacecited by 15
  5. 2024Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning ratescited by 14
  6. 2022Deep neural network expressivity for optimal stopping problemscited by 9
  7. 2022Mean-field neural networks-based algorithms for McKean-Vlasov control problems *cited by 9
  8. 2022Neural Q-learning for solving PDEscited by 8
  9. 2024An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learningcited by 6
  10. 2025A brief review of the Deep BSDE method for solving high-dimensional partial differential equationscited by 5
  11. 2022Temporal Difference Learning with Continuous Time and State in the Stochastic Settingcited by 4
  12. 2023Simultaneous upper and lower bounds of American-style option prices with hedging via neural networkscited by 3
14 more
  1. 2024Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networkscited by 3
  2. 2025One model to solve them all: 2BSDE families via neural operatorscited by 3
  3. 2023Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Studycited by 2
  4. 2024P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimizationcited by 2
  5. 2022On Parametric Optimal Execution and Machine Learning Surrogatescited by 1
  6. 2023Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equationscited by 1
  7. 2023Deep Learning for Mean Field Optimal Transportcited by 1
  8. 2023Quantile and moment neural networks for learning functionals of distributionscited by 1
  9. 2023Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustnesscited by 1
  10. 2024An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Controlcited by 1
  11. 2025PADAM: Parallel averaged Adam reduces the error for stochastic optimization in scientific machine learningcited by 1
  12. 2025Error analysis for the deep Kolmogorov methodcited by 0
  13. 2026Random Neural Network Expressivity for Non-Linear Partial Differential Equationscited by 0
  14. 2026Deep numerical schemes for systems of Ergodic BSDEs with applications to regime-switching forward utilitiescited by 0