Research Interests
Justin is an Associate Professor of Mathematics at the University of Oxford, where he is a faculty member of the Mathematical Finance and Data Science Groups. His research is at the intersection of Applied Mathematics, Machine Learning, and High Performance Computing. His recent research has focused on the mathematical theory and applications of Deep Learning.
Justin develops deep learning models for large financial datasets such as: highfrequency data from limit order books, loans, and options. He is also developing deep learning methods for constructing partial differential equation (PDE) models from data, which has a variety of applications in science, engineering, and finance. This includes recent work on developing deep learningbased PDE models as reducedorder simulations for "computationallychallenging physics" involving turbulent flows, whose accurate modeling is critical for flight vehicle design.
Justin received his PhD from Stanford University and holds a Bachelors degree from Princeton University. He was a Chapman Fellow at the Department of Mathematics at Imperial College. He was awarded the 2014 SIAM Financial Mathematics and Engineering Conference Paper Prize.
Current research projects include:
 Computational methods, machine learning algorithms, and stochastic models in financial mathematics
 Asymptotic analysis of deep neural networks (e.g., law of large numbers, central limit theorems, and large deviation principles)
 Applications of deep learning to partial differential equation models
 Stochastic online algorithms for optimizing over highdimensional computationallyintensive simulations
Courses
 Introduction to Machine Learning (Imperial College Math Dept., Spring 2016): Master/PhD level course on machine learning.
 Deep Learning (University of Illinois at UrbanaChampaign): Master/PhD level course on deep learning. Topics include convolution neural networks, recurrent neural networks, and deep reinforcement learning. Homeworks and projects on image classification, video recognition, and deep reinforcement learning. Training of deep learning models using TensorFlow and GPUs. Supported by a computational grant from a national supercomputer. Course website
 Deep Learning II (University of Illinois at UrbanaChampaign): Deep learning applications in (1) reinforcement learning, (2) image recognition, and (3) highfrequency models of financial markets. There will be a special focus on distributed training of deep learning models. Supported by a computational grant from Microsoft.
Publications
 "Continuoustime stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations" (with Z. Wang), 2022.
 "Global Convergence of the ODE Limit for Online ActorCritic Algorithms in Reinforcement Learning" (with Z. Wang), 2021.
 "PDEconstrained Models with Neural Network Terms: Optimization and Global Convergence" (with J. MacArt and K. Spiliopoulos). Major Revision at Journal of Computational Physics, 2021.
 "Mean Field Analysis of Deep Neural Networks" (with K. Spiliopoulos). Mathematics of Operations Research, accepted 2020.
 "Online Adjoint Methods for Optimization of PDEs" (with K. Spiliopoulos). Applied Mathematics and Optimization, In Press, 2022.
 "Deep Learning Closure of the NavierStokes Equations for Transitional Flows" (with J. F. MacArt and M. Panesi). Proceedings of AIAA Scitech, 2022.
 "Deep Learning for Mortgage Risk" (with A. Sadhwani and K. Giesecke). Journal of Financial Econometrics, 2021.
 "Mean Field Analysis of Neural Networks: A Law of Large Numbers" (with K. Spiliopoulos).
SIAM Journal on Applied Mathematics, 2020.
 "Inference for large financial systems" (with G. Schwenkler and K. Giesecke). Mathematical Finance, 2020.
 "Asymptotics of Reinforcement Learning with Neural Networks" (with K. Spiliopoulos). Accepted, Stochastic Systems, 2020.
 "DGM: A deep learning algorithm for solving partial differential equations" (with K. Spiliopoulos). Journal of Computational Physics, 2018.
 "Mean Field
Analysis of Neural Networks: A Central Limit Theorem" (with K. Spiliopoulos). Stochastic Processes and their Applications, 2019.
 "Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem" (with K. Spiliopoulos). Stochastic Systems, 2020.
 "Universal features of price formation in financial markets: perspectives from Deep Learning"
(with Rama Cont). Media coverage: Risk Magazine. Quantitative Finance, 2019.
 "Stochastic Gradient Descent in Continuous Time" (with K. Spiliopoulos). SIAM Journal on Financial Mathematics,
8(1), 933–961, 2017.
 "DPM: A deep learning PDE augmentation method with application to largeeddy simulation" (with J. Freund and J. MacArt). Datasets. Journal of Computational Physics, 2020.
 "Embedded training of neuralnetwork subgridscale turbulence models" (with J. MacArt and J. Freund). Physical Review of Fluids, In Press, 2020.
 "Deep Learning for Limit Order Books". Quantitative Finance, 2018.
 "Risk Analysis for Large Pools of Loans" (with K. Giesecke). Winner of SIAM
Financial Mathematics and Engineering Conference Paper Prize. Management Science, 2018.
 "Deep Learning Models in Finance". Invited article for SIAM News, June 2017.
 "Fluctuation Analysis for the Loss from
Default" (with K. Giesecke and K. Spiliopoulos).
Stochastic Processes and their Applications, (124): 23222362, 2014.
 "Largescale Loan Portfolio Selection" (with K. Giesecke and
G. Tsoukalas). Operations Research, 2016.
 "Large Portfolio Asymptotics for Loss From
Default" (with K. Giesecke, K. Spiliopoulos, and R. Sowers).
Mathematical Finance, 2015.
 "Optimization of SecondaryAir Addition in a Continuous OneDimensional Spray Combustor" (with L. Rodriquez, A. Sideris, and W. Sirignano). Journal of Propulsion and Power, 2010.
 "A ForwardBackward Algorithm for Stochastic Control Problems" (with S. Ludwig, R. Huang, and G. Papanicolaou).
Proceedings of the First International Conference on Operations Research and Enterprise Systems. Vilamoura, Portugal.
 Book Review on deep learning, SIAM Review, 60(3), September 2018.
Grants
 CoPI for Department of Energy PSAAP III Center (~$17 million, 20202021).
 Blue Waters supercomputer, 44 million core hours, value of $860,631.
 Summit supercomputer, 120,000 GPU hours.
Supervision of PhD Theses
 Lei Fan (ISE, UIUC, 2021). PhD Thesis: "Machine Learning Methods for Pricing and Hedging Financial Derivatives." Job Placement: J.P. Morgan Systematic Trading.
 Xiaobo Dong (ISE, UIUC, 2021). PhD Thesis: "Deep Reinforcement Learning Models of High Frequency Financial Data." Job Placement: J.P. Morgan Machine Learning.
 Ziheng Wang (Math, Oxford, 2024). PhD Thesis: "Asymptotic Analysis of Deep Reinforcement Learning." PhD funded by HSBC.
 Filippo De Angelis (Math, Oxford, 2024). PhD Thesis on machine learning models and methods in financial mathematics. PhD funded by HSBC.
 Deqing Jiang (Math, Oxford, 2024). PhD Thesis on deep reinforcement learning and mathematical finance. PhD funded by Alan Turing Institute.
 Additional supervised research: Yunxiang Zhang (supervised undergraduate thesis; now a PhD student at Cornell ORIE), Giri Tarun, Abhinav (supervised MS thesis; now a PhD student at UIUC CS), and Rachneet Kaur (PhD candidate at UIUC).
Presentations to Industry
 Google Deepmind, Paris, January 2022.
 Two Sigma Investments, New York City, January 2020.
 Maven Securities, London, October 2020.
 J.P. Morgan, New York City, August 2017. Deep Learning in Finance.
 Bank of England, London, May 2016. Machine Learning for Loan Risk.
 Winton Capital Management, London, January 2016. Modeling financial data with Neural Networks.
 Capital Fund ManagementImperial Workshop, London, September 2015. Risk Analysis for Loan Portfolios.
 Lending Club, San Francisco, June 2015. Risk Analysis for Loan Portfolios.
Professional Service
 Associate Editor, Mathematical Finance.
 Managing Editor, Quantitative Finance.
 Associate Editor, Journal of Dynamics and Games (an AIMS journal).
 Associate Editor, Special Issue of Management Science on Data Science.
 Currently, I am the director of the MSc program in Mathematical & Computational Finance at the University of Oxford.
 Coorganized an internship program for students with banks, investment companies, and hedge funds. (Participating companies include Citadel, JP Morgan, Nomura, BNP Paribas, Citibank, and EDF Trading.) The quantitative research conducted during the internship is part of the students' MSc thesis.
 Organized the "Careers in Quantitative Finance" seminar series where companies present internship and job opportunities to the students. Participants include JP Morgan, Nomura, Deutsche Bank, Citibank, EDF Trading, Mazars, and NatWest Markets (formerly Royal Bank of Scotland).
 Introduced new courses/topics on deep learning and highperformance computing to develop models on largescale financial datasets.
 Increased the number of applicants by 200% to almost 750 total applicants per year and increased number of enrolled students by almost 30%.
 Invited to organize minisymposium at SIAM Annual Meeting, Toronto, 2020.
 Machine Learning minisymposium at SIAM Financial Mathematics Conference, Toronto, 2019.
 Machine Learning for Finance minisymposium at SIAM Financial Mathematics Conference, Austin, November 2016.
 Machine learning in Finance session at INFORMS Annual Meeting, Houston, October 2017.
 Financial engineering session at INFORMS Applied Probability Meeting, Northwestern University, July 2017.
 Machine Learning for Finance session at INFORMS Annual Meeting, Nashville, November 2016.
 Largescale Portfolio Risk session at INFORMS Annual Meeting, Philadelphia, November 2015.
 Reviewer for SIAM Journal on Applied Mathematics, SIAM Journal on Financial Mathematics, Journal of Machine Learning Research, Constructive Approximation (Special Issue on Deep Learning), NeurIPS, Operations Research, Stochastic Systems, and Management Science.
Seminar and Conference Presentations
 Google Deepmind, Paris, January 2022.
 Isaac Newton Institute, University of Cambridge, November 2021.
 London Business School, December 2021.
 Department of Applied Mathematics, Brown University, November 2021.
 Department of Mathematics, UCLA, February 2021.
 SIAM Conference on Dynamical Systems, 2021. Invited Speaker.
 SIAM Conference on Financial Mathematics, 2021. Invited Speaker.
 Seminar, Department of Physics, University of Oxford, November 2020.
 NSF Workshop on Machine Learning in Transport Phenomena in Dallas, Texas, 2020. Distinguished Speaker.
 Department of Mathematics, University of Minnesota, February 2021.
 Two Sigma Investments, New York City, January 2020. Invited Seminar.
 Workshop on Machine Learning in Finance at the University of Toronto, 2019. Invited Speaker.
 Theory of Deep Learning Workshop, Alan Turing Institute, London, 2020. Invited Speaker.
 Department of Mathematics, UCLA, Colloquium, 2019. Deep Learning: Applications and Asymptotics.
 Department of Mathematics, University of Michigan, 2019.
 Department of Mathematics, Oxford University, Data Science Seminar, 2019.
 Department of Mathematics, Oxford University, Financial Mathematics Seminar, 2019.
 Department of Statistics, Carnegie Mellon University, January 2019.
 Department of Industrial Engineering & Operations Research, Columbia University, February 2019.
 Department of Management Science & Engineering, Stanford University, 2019.
 Department of Mathematics, Washington University in St. Louis, 2019.
 BIRS Workshop on Modern Challenges between Financial Mathematics, Financial Technology, and Financial Economics. Banff, Canada, 2020. Invited Talk.
 American Institute of Mathematics/NSF Workshop on "Deep Learning and PDEs", 2019.
 Department of Statistics, Purdue University, 2019.
 SIAM Conference on Financial Math, Toronto, June 2019.
 INFORMS Annual Meeting, Seattle, October 2019.
 Department of Mathematics, Univ. of Illinois Urbana Champaign, Sept. 2018. Mean Field Analysis of Neural Networks in Machine Learning.
 SIAM Annual Conference, July 2018.
 London Quantitative Finance Seminar, May 2018. Deep Learning Models of High Frequency Financial Data.
 Seminar at the Department of Applied Math at the University of Colorado Boulder, April 2018.
 Deep Learning conference at the National Center for Supercomputing Applications, 2017. Deep Learning for PDEs.
 Seminar at Princeton University, 2017. Machine Learning in Finance.
 J.P. Morgan, Machine Learning and AI Forum seminar, August 2017. Deep Learning in Finance.
 Seminar at Northwestern University, April 2017.
 Seminar at UIUC Machine Learning Seminar Series, March 2017.
 Seminar at UIUC Business School, February 2017. Deep Learning for Modeling Limit Order Books.
 SIAM Financial Mathematics Conference, Austin, Texas, November 2016.
 Seminar at London Business School, London, June 2016. Deep Learning for Modeling Limit Order Books.
 Seminar at Oxford University, May 2016. Deep Learning for Modeling Financial Data.
 Statistics Seminar at Imperial College, London, May 2016. Deep Learning for Modeling Financial Data.
 INFORMS Annual Meeting, Philadelphia, November 2015. Invited Speaker and Organizer of Largescale Portfolio Risk Session.
 Finance and Stochastics Seminar at Imperial College, London, October 2015.
 LondonParis Bachelier Workshop on Mathematical Finance, London, September 2015. Invited Speaker.
 IPAM Workshop on Systemic Risk and Financial Networks, Los
Angeles, 2015.
 SIAM Financial Mathematics and Engineering Meeting, Chicago,
2014. Invited Speaker.
 INFORMS Annual Meeting, San Francisco, 2014. Invited Speaker
and Organizer of Financial Risks Session.
 Likelihood Estimation for Large Financial Systems. Joint Mathematics Meeting, Baltimore, 2014. Invited Speaker.
 Fluctuation Analysis
for Loss from Default. INFORMS
Annual Meeting, Minneapolis, 2013. Invited Speaker.
 Lecture on Subprime Crisis. For a general audience at Stanford University, 2013.
 Fifth Western Conference on Mathematical Finance, Stanford University, 2013. Invited Speaker.
 INFORMS Annual Meeting, Phoenix, October, 2012. Invited Speaker.
 Financial Mathematics Seminar, Stanford University, 2012. Invited Speaker.
 SIAM Financial Mathematics and Engineering Meeting, Minneapolis, 2012. Chair of Credit Risk Session.
 Annual Meeting of the Canadian Applied and Industrial Mathematics Society, Toronto, 2012. Invited Speaker.
 5th Financial Risks International Forum, Paris, France, 2012.
