Ariel Neufeld
Ariel Neufeld
Associate Professor


Nanyang Technological University (NTU)
Division of Mathematical Sciences
Office SPMS-MAS 05-02
21 Nanyang Link, Singapore 637371
Phone (65) 6592 1799
Email ariel.neufeld@ntu.edu.sg



I am a tenured Associate Professor in mathematics at the Nanyang Technological University in Singapore.
I received my PhD from ETH Zurich in 2015 under the supervision of Prof. Marcel Nutz and Prof. Martin Schweizer.

My research focuses on:

• Numerical methods for high-dimensional nonlinear PDEs
• Artificial intelligence theory
• Financial and insurance mathematics under model uncertainty
• Stochastic analysis and stochastic optimal control
• Stochastic optimization and applied probability theory

Current support by the following grants is gratefully acknowledged:

• MOE AcRF Tier 2 Grant   MOE-T2EP20222-0013
• MOE AcRF Tier 1 Grant   RG74/21

A detailed CV can be found here.

Open Positions

I am looking for Postdocs, PhD students, as well as Bachelor/Master students who would like to join my research group; see for example

AI-for-X Postdoc position

Postdoc position

PhD position

Research Internship position for PhD and master students

If you would like to join my research group (even if you do not see a suitable job announcement), please feel free to contact me anytime by email.

Members of the Research Group

• Jonas Gebele   (PhD Student with a Nanyang President's Graduate Scholarship, since 08.2025)

• Kyunghyun Park   (Gopalakrishnan - Presidential Postdoctoral Fellow, since 12.2022)

• Thanh Phong Pham   (Undergraduate Research Student, since 07.2025; jointly supervised also by Qikun Xiang)

• Philipp Schmocker   (PhD Student, since 08.2021; has submitted his PhD thesis with expected PhD defense end of 2025, now PostDoc at ETH Zurich)

• Xuanye Song   (Visiting Postdoctoral Research Fellow, since 07.2025)

• Viet Khoa Tran   (Undergraduate Research Student, since 08.2024; jointly supervised also by Philipp Schmocker)

• Qikun Xiang   (Postdoctoral Research Fellow, started 08.2019 as PhD student and 01.2024 as PostDoc)

Former Members of the Research Group

• Géraldine Bouveret   (Gopalakrishnan - Presidential Postdoctoral Fellow, 11.2019-01.2022; now Chief Research Officer at RIMM Sustainability)

• Zeyi Chen   (Undergraduate Research Student, 08.2022-07.2024, jointly supervised also by Qikun Xiang; now PhD student at INSEAD)

• Pushpendu Ghosh   (Research Internship, 08.2019-12.2019; now Applied Scientist at Amazon)

• Johannes Langner   (Visiting PhD Student, 10.2023-05.2024, jointly supervised also by Kyunghyun Park; now PhD student at Leibniz University of Hannover)

• Yongming Li   (Project Officer, 05.2020-12.2020; now PhD student in mathematics at Texas A&M University)

• Matthew Ng Cheng En   (Project Officer, 08.2021-07.2023; now Quant at BNP Paribas)

• Thi Van Hang Nguyen   (Postdoctoral Research Fellow, SASEA Fellowship, 10.2022-09.2024; now Senior Scientist at VIASM)

• Tuan Anh Nguyen   (Postdoctoral Research Fellow, 01.2023-03.2024; now Senior Scientist at University of Bielefeld)

• Julian Sester   (Postdoctoral Research Fellow, 04.2020-06.2022; now Assistant Professor in mathematics at NUS)

• Alessandro Sgarabottolo   (Visiting PhD Student, 02.2024-09.2024; jointly supervised also by Kyunghyun Park; now PhD student at University of Bielefeld)

• Shunan Sheng   (Undergraduate Research Student, 06.2020-07.2022; now PhD student in statistics at Columbia University)

• Sizhou Wu   (Postdoctoral Research Fellow, 08.2021-08.2024; now Assistant Professor in mathematics at Shanghai University of Finance and Economics)

• Daiying Yin   (Undergraduate Research Student, 06.2020-08.2021; now PhD student in mathematics at NTU with J.-P. Ortega)

• Ying Zhang   (Postdoctoral Research Fellow, 11.2020-06.2023; now Assistant Professor in mathematics at HKUST-GZ)

Teaching

Stochastic Processes MH 3512

Introduction
Indicator Function
Conditional Expectation
Monotone Convergence & Dominated Convergence Theorem
Lecture notes (many thanks to N. Privault)
Lecture notes (same, but marked)

Publications and Preprints

A. Kratsios, A. Neufeld, P. Schmocker:
Generative neural operators of log-complexity can simultaneously solve infinitely many convex programs
Preprint (submitted), 2025 [PDF, arXiv, Code]

Z. Chen, A. Neufeld, Q. Xiang:
Provably convergent stochastic fixed-point algorithm for free-support Wasserstein barycenter of continuous non-parametric measures
Preprint (submitted), 2025 [PDF, arXiv, Code]

A. Neufeld, T. A. Nguyen, P. Schmocker:
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion
Preprint (submitted), 2025 [PDF, arXiv, Code]

A. Neufeld, P. Schmocker:
Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion
Preprint (submitted), 2024 [PDF, arXiv, Code]

J. Langner, A. Neufeld, K. Park:
Markov-Nash equilibria in mean-field games under model uncertainty
Preprint (submitted), 2024 [PDF, arXiv, Code]

A. Neufeld, T. A. Nguyen:
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in Lp-sense
Preprint (submitted), 2024 [PDF, arXiv]

L. Liang, A. Neufeld, Y. Zhang:
Non-asymptotic convergence analysis of the stochastic gradient Hamiltonian Monte Carlo algorithm with discontinuous stochastic gradient with applications to training of ReLU neural networks
Preprint (submitted), 2024 [PDF, arXiv, Code]

A. Neufeld, Y. Zhang:
Non-asymptotic estimates for accelerated high order Langevin Monte Carlo algorithms
Preprint (submitted), 2024 [PDF, arXiv, Code]

D. Bartl, A. Neufeld, K. Park:
Numerical method for nonlinear Kolmogorov PDEs via sensitivity analysis
Preprint (submitted), 2024 [PDF, arXiv, Code]

A. Neufeld, M. Ng, Y. Zhang:
Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems
Preprint (submitted), 2024 [PDF, arXiv, Code]

A. Neufeld, P. Schmocker:
Universal approximation property of Banach space-valued random feature models including random neural networks
Preprint (submitted), 2023 [PDF, arXiv, Code]

A. Neufeld, Q. Xiang:
Feasible approximation of matching equilibria for large-scale matching for teams problems
Preprint (submitted), 2023 [PDF, arXiv, Code]

J. Chen, Y. Li, A. Neufeld:
Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its complexity analysis
Preprint (submitted), 2023 [PDF, arXiv, Code]

A. Neufeld, P. Schmocker:
Chaotic Hedging with Iterated Integrals and Neural Networks
Preprint (submitted), 2022 [PDF, arXiv, Code]

A. Neufeld, Q. Xiang:
Numerical method for approximately optimal solutions of two-stage distributionally robust optimization with marginal constraints
Preprint (submitted), 2022 [PDF, arXiv, Code]

A. Neufeld, Q. Xiang:
Numerical method for feasible and approximately optimal solutions of multi-marginal optimal transport beyond discrete measures
Preprint (submitted), 2022 [PDF, arXiv, Code]

C. Beck, S. Becker, P. Cheridito, A. Jentzen, A. Neufeld:
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems
Preprint (submitted), 2020 [PDF, arXiv, Code]



D. Bartl, A. Neufeld, K. Park:
Sensitivity of robust optimization problems under drift and volatility uncertainty
Finance and Stochastics, accepted for publication, 2025 [PDF, arXiv]

A. Neufeld, J. Sester:
Non-concave stochastic optimal control in finite discrete time under model uncertainty
Mathematical Finance, accepted for publication, 2025 [PDF, arXiv, Code]

A. Neufeld, P. Schmocker:
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
Analysis and Applications, accepted for publication, 2025 [PDF, arXiv]



H. H. S. Chittoor, P. R. Griffin, A. Neufeld, J. Thompson, M. Gu:
QuLTSF: Long-Term Time Series Forecasting with Quantum Machine Learning
Proceedings of the 17th International Conference on Agents and Artificial Intelligence (ICAART 2025), Vol. 1, pp. 824-829, 2025 [PDF, arXiv, DOI, Code]

A. Neufeld, P. Schmocker, S. Wu:
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
Communications in Nonlinear Science and Numerical Simulation, Vol. 143, 108556, 2025 [PDF, arXiv, DOI, Code]

A. Neufeld, T. A. Nguyen:
Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations
Communications in Mathematical Sciences, Vol. 23, No. 4, pp. 883-912, 2025 [PDF, arXiv, DOI]

A. Neufeld, T. A. Nguyen:
Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean-Vlasov stochastic differential equations
Journal of Mathematical Analysis and Applications, Vol. 541, No. 1, 128661, 2025 [PDF, arXiv, DOI]

A. Neufeld, T. A. Nguyen, S. Wu:
Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities
Journal of Complexity, Vol. 90, 101946, 2025 [PDF, arXiv, DOI]

A. Neufeld, T. A. Nguyen, S. Wu:
Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations
Analysis and Applications, Vol. 23, No. 07, pp. 1227-1278, 2025 [PDF, arXiv, DOI]

A. Neufeld, S. Wu:
Multilevel Picard algorithm for general semilinear parabolic PDEs with gradient-dependent nonlinearities
Journal of Numerical Mathematics, 2025 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester:
Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems
Journal of Applied Probability, Vol. 62, No. 2, pp. 558-571, 2025 [PDF, arXiv, DOI, Code]

D.-Y. Lim, A. Neufeld, S. Sabanis, Y. Zhang:
Langevin dynamics based algorithm e-THεO POULA for stochastic optimization problems with discontinuous stochastic gradient
Mathematics of Operations Research, Vol. 50, No. 3, pp. 2333-2374, 2025 [PDF, arXiv, DOI, Code]

A. Neufeld, M. Ng, Y. Zhang:
Non-asymptotic convergence bounds for modified tamed unadjusted Langevin algorithm in non-convex setting
Journal of Mathematical Analysis and Applications, Vol. 543, No. 1, 128892, 2025 [PDF, arXiv, DOI, Code]

A. Neufeld, S. Wu:
Multilevel Picard approximation algorithm for semilinear partial integro-differential equations and its complexity analysis
Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 13, pp. 1220–1278, 2025 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester:
Neural networks can detect model-free static arbitrage strategies
Applied Mathematics and Optimization, Vol. 90, 41, 2024 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester:
Robust Q-learning Algorithm for Markov Decision Processes under Wasserstein Uncertainty
Automatica, Vol. 168, 111825, 2024 [PDF, arXiv, DOI, Code]

S. Sheng, Q. Xiang, I. Nevat, A. Neufeld:
Binary Spatial Random Field Reconstruction from Non-Gaussian Inhomogeneous Time-series Observations
Journal of the Franklin Institute, Vol. 361, No. 2, pp. 612-636, 2024 [PDF, arXiv, DOI, Code]

J. Ansari, E. Lütkebohmert, A. Neufeld, J. Sester:
Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information
Finance and Stochastics, Vol. 28, No. 4, pp. 911-964, 2024 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester, D. Yin:
Detecting data-driven robust statistical arbitrage strategies with deep neural networks
SIAM Journal on Financial Mathematics (SIFIN), Vol. 15, No. 2, pp. 436-472, 2024 [PDF, arXiv, DOI, Code]

D.-Y. Lim, A. Neufeld, S. Sabanis, Y. Zhang:
Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function
IMA Journal of Numerical Analysis, Vol. 44, No. 3, pp. 1464-1559, 2024 [PDF, arXiv, DOI, Code]

Q. Xiang, A. Neufeld, G. W. Peters, I. Nevat, A. Datta:
A Bonus-Malus Framework for Cyber Risk Insurance and Optimal Cybersecurity Provisioning
European Actuarial Journal, Vol. 14, pp. 581-621, 2024 [PDF, arXiv, DOI, Code]

C. Beck, S. Becker, P. Cheridito, A. Jentzen, A. Neufeld:
An efficient Monte Carlo scheme for Zakai equations
Communications in Nonlinear Science and Numerical Simulation, Vol. 126, 107438, 2023 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester, M. Sikic:
Markov Decision Processes under Model Uncertainty
Mathematical Finance, Vol. 33, No. 3, pp. 618-665, 2023 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester:
A deep learning approach to data-driven model-free pricing and to martingale optimal transport
IEEE Transactions on Information Theory, Vol. 69, No. 5, pp. 3172-3189, 2023 [PDF, arXiv, DOI, Code]

A. Neufeld, A. Papapantoleon, Q. Xiang:
Model-free bounds for multi-asset options using option-implied information and their exact computation
Management Science, Vol. 69, No. 4, pp. 2051-2068, 2023 [PDF, arXiv, DOI, Code]

M. Baes, C. Herrera, A. Neufeld, P. Ruyssen:
Low-Rank plus Sparse Decomposition of Covariance Matrices using Neural Network Parametrization
IEEE Transactions on Neural Networks and Learning Systems, Vol. 34, No. 1, pp. 171-185, 2023 [PDF, arXiv, DOI, Code]

P. Ghosh, A. Neufeld, J. K. Sahoo:
Forecasting directional movements of stock prices for intraday trading using LSTM and random forests
Finance Research Letters, Vol. 46, Part A, 102280, 2022 [PDF, arXiv, DOI, Code]

A. Neufeld, J. Sester:
On the stability of the martingale optimal transport problem: A set-valued map approach
Statistics & Probability Letters, Vol. 176, pp. 109131-1-7, 2021 [PDF, arXiv, DOI]

A. Neufeld, J. Sester:
Model-free price bounds under dynamic option trading
SIAM Journal on Financial Mathematics (SIFIN), Vol. 12, No. 4, pp. 1307-1339, 2021 [PDF, arXiv, DOI, Code]

D. Bartl, M. Kupper, A. Neufeld:
Duality Theory for Robust Utility Maximisation
Finance and Stochastics, Vol. 25, No. 3, pp. 469-503, 2021 [PDF, arXiv, DOI]

P. J. Graber, V. Ignazio, A. Neufeld:
Nonlocal Bertrand and Cournot Mean Field Games with General Nonlinear Demand Schedule
Journal de Mathématiques Pures et Appliquées (JMPA), Vol. 148, pp. 150-198, 2021 [PDF, arXiv, DOI]

P. Harms, C. Liu, A. Neufeld:
Supermartingale Deflators in the Absence of a Numéraire
Mathematics and Financial Economics, Vol. 15, pp. 885-915, 2021 [PDF, arXiv, DOI]

C. Beck, S. Becker, P. Cheridito, A. Jentzen, A. Neufeld:
Deep splitting method for parabolic PDEs
SIAM Journal on Scientific Computing (SISC), Vol. 43, No. 5, pp. A3135-A3154, 2021 [PDF, arXiv, DOI, Code]

A. Jentzen, B. Kuckuck, A. Neufeld, P. von Wurstemberger:
Strong error analysis for stochastic gradient descent optimization algorithms
IMA Journal of Numerical Analysis, Vol. 41, No. 1, pp. 455-492, 2021 [PDF, arXiv, DOI]

D. Bartl, M. Kupper, A. Neufeld:
Pathwise superhedging on prediction sets
Finance and Stochastics, Vol. 24, No. 1, pp. 215-248, 2020 [PDF, arXiv, DOI]

T. Fadina, A. Neufeld, T. Schmidt:
Affine processes under parameter uncertainty
Probability, Uncertainty and Quantitative Risk, Vol. 4, No. 1, pp. 1-35, 2019 [PDF, arXiv, DOI]

D. Bartl, M. Kupper, A. Neufeld:
Stochastic integration and differential equations for typical paths
Electronic Journal of Probability, Vol. 24, No. 97, pp. 1-21, 2019 [PDF, arXiv, DOI]

A. Neufeld, M. Sikic:
Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty
Mathematical Methods of Operations Research, Vol. 90, No. 2, pp. 229-253, 2019 [PDF, arXiv, DOI]

C. Liu, A. Neufeld:
Compactness Criterion for Semimartingale Laws and Semimartingale Optimal Transport
Transactions of the American Mathematical Society, Vol. 372, No. 1, pp. 187-231, 2019 [PDF, arXiv, DOI]

A. Neufeld:
Buy-and-Hold Property for Fully Incomplete Markets when Super-replicating Markovian Claims
International Journal of Theoretical and Applied Finance, Vol. 21, No. 8, 1850051, 2018 [PDF, arXiv, DOI]

A. Neufeld, M. Sikic:
Robust Utility Maximization in Discrete-Time Markets with Friction
SIAM Journal on Control and Optimization (SICON), Vol. 56, No. 3, pp. 1912-1937, 2018 [PDF, arXiv, DOI]

Y. Dolinsky, A. Neufeld:
Super-replication in Fully Incomplete Markets
Mathematical Finance, Vol. 28, No. 2, pp. 483-515, 2018 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Robust Utility Maximization with Lévy Processes
Mathematical Finance, Vol. 28, No. 1, pp. 82-105, 2018 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Nonlinear Lévy Processes and their Characteristics
Transactions of the American Mathematical Society, Vol. 369, No. 1, pp. 69-95, 2017 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Measurability of Semimartingale Characteristics with Respect to the Probability Law
Stochastic Processes and their Applications, Vol. 124, No. 11, pp. 3819-3845, 2014 [PDF, arXiv, DOI]

A. Neufeld, M. Nutz:
Superreplication under Volatility Uncertainty for Measurable Claims
Electronic Journal of Probability, Vol. 18, No. 48, pp. 1-14, 2013 [PDF, arXiv, DOI]

K. Du, A. Neufeld:
A note on asymptotic exponential arbitrage with exponentially decaying failure probability
Journal of Applied Probability, Vol. 50, No. 3, pp. 801-809, 2013 [PDF, arXiv, DOI]

Theses

A. Neufeld:
Knightian Uncertainty in Mathematical Finance
PhD Thesis ETH Zurich, Diss. ETH No. 22605, 2015 [PDF, ETH e-collection]

Miscellaneous

The Oracle of DLPhi [PDF]

This manuscript has mostly humouristic value. However, while the main theorem is based on a dubious application of the axiom of choice, it is a correct mathematical statement.
Therefore, this manuscript at least highlights the dangers of applying mathematical theory to real-world applications blindly. 
Last update: September 16, 2025