Ph.D. Training

Fundamental areas:

• Stochastic analysis: foundations and new directions
• Stochastic partial differential equations
• Optimization, optimal transport, and stochastic control
• Differential games, large population dynamic systems, and mean-field limit
• Risk analysis and uncertainty quantification
• Computational methods for complex systems
• Theoretical foundation of machine learning
• Information Geometry

Application areas:

• Market microstructure and high-frequency trading
• Risk management and robust hedging
• Financial stability and systemic risk
• Energy markets: risk management and mechanism design
• Sustainability, green finance, and climate risks
• Digital finance and blockchains
• Market interactions, regulation, and optimal incentive
• Machine learning and generative models
• Monte Carlo simulation and digital twins
   

The FRE department contributes to the ECE Ph.D. program with the following courses:

• FRE-GY 6233, Option pricing and stochastic calculus, by N.Touzi
• FRE-GY 9073, Stochastic systems and modern machine learning theory, by R. Xu
• FRE-GY 7821/ECE-GY 9211, Stochastic control and finance, by N. Touzi
• FRE-GY 9733, Dynamic optimization under strategic interactions, by X. Zhang
• Information Geometry and Its Applications in Machine Learning and Beyond, by A. Aboussalah

Relevant Courses from ECE:

• ECE-GY 6063, Information theory
• ECE-GY 6113, Digital signal processing I  
• ECE-GY 6143, Machine learning
• ECE-GY 6243, System theory and feedback control 
• ECE-GY 6263, Game theory 
• ECE-GY 6303, Probability theory and stochastic processes 
• ECE-GY 6363, Data center and cloud computing
• ECE-GY 6623, Smart grids: control, economics, planning and regulation
• ECE-GY 7123, Deep learning
• ECE-GY 7143, Advanced machine learning 
• ECE-GY 8223, Applied nonlinear control 
• ECE-GY 9123, Selected topics in signal processing

Ph.D. students are eligible to register for courses offered by other departments within the University. For instance, you may consider the following courses from the Courant Institute.

• MATH-GA 2911, Probability Theory I,II 
• MATH-GA 2701, Methods of Applied Math 
• MATH-GA 2704, Applied stochastic analysis 
• MATH-GA 2500, Partial differential equations
• MATH-GA 2931, Advanced topics in probability: random matrix universality 
• MATH-GA 2012, Advanced topics in numerical analysis: convex and nonsmooth optimization 
• MATH-GA 2830, Advanced topics in applied math: theory of deep learning

Together with Columbia University's Department of Industrial Engineering and Operations Research (IEOR), the FRE Department organizes the monthly Columbia-NYU Financial Engineering Colloquium. 

The Peter Carr Seminar Series is held monthly and aims to bring cutting-edge research from the financial industry to the FRE department. We are also organizing a special seminar series inviting well-established researchers worldwide. 

Amine Aboussalah
Industry Assistant Professor

Agnès Tourin
Industry Professor

Nizar Touzi
Professor

Renyuan Xu
Assistant Professor

Xin Zhang
Assistant Professor

In order to receive training through the FRE Department, you must apply to the ECE Ph.D. Program. Please mention potential FRE Ph.D. mentors in your application and feel free to contact the ECE Department via email.