Xin Zhang

Hello, my name is Xin Zhang. Currently, I am a tenure-track assistant professor at the FRE department of NYU. Before that, I was a university assistant in the group of Prof. Mathias Beiglböck at the University of Vienna from 2021 to 2024. I obtained my Ph.D. in Mathematics under the supervision of Prof. Erhan Bayraktar at the University of Michigan in 2021, and my B.S. in Mathematics at Fudan University in 2016.

My research focuses on optimal transport, stochastic analysis and control, as well as their applications in Finance and Machine Learning. More specifically, I am interested in viscosity solution of nonlinear PDE, and optimal transport in robust finance. Here is my Curriculum Vitae and email address xz1662@nyu.edu.

Preprints and Publications (see also Google Scholar)

Cylindrical Projections of Occupied Diffusions, with Valentin Tissot-Daguette. [ArXiv]
Scaling Limits for Exponential Hedging in Trinomial Models, with Yan Dolinsky. [ArXiv]
The Wasserstein Space of Stochastic Processes in Continuous Time, with Daniel Bartl, Mathias Beiglböck, Gudmund Pammer, Stefan Schrott. [ArXiv]
Exciting games and Monge-Ampère equations, with Julio Backhoff and Zhizhang Wang. [ArXiv]
Representing General Stochastic Processes as Martingale Laws, with Mathias Beiglböck, Gudmund Pammer, Stefan Schrott. [ArXiv]
Reciprocal Specific Relative Entropy between Continuous Martingales, with Julio Backhoff, to appear in Electronic Communications in Probability. [ArXiv]
Viscosity Solutions of Fully second-order HJB Equations in the Wasserstein Space, with Erhan Bayraktar, Hang Cheung, Ibrahim Ekren, Jinniao Qiu, Ho Man Tai, to appear in SIAM Journal on Control and Optimization. [ArXiv]
Scaling Limits for Exponential Hedging in the Brownian Framework, with Yan Dolinsky, SIAM Journal on Control and Optimization (2026). [ArXiv] [Article]
Comparison for semi-continuous Viscosity Solutions for second order PDEs on the Wasserstein Space, with Erhan Bayraktar, Ibrahim Ekren, and Xihao He, Journal of Differential Equations (2026). [ArXiv] [Article]
Specific Wasserstein Divergence between Continuous Martingales, with Julio Backhoff, Mathematics of Operations Research (2026). [ArXiv] [Article]
Walsh Spider Diffusions as Time Changed Multi-parameter Processes, with Erhan Bayraktar and Jingjie Zhang, Stochastic Processes and their Applications (2025). [ArXiv] [Article]
Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space, with Erhan Bayraktar and Ibrahim Ekren, SIAM Journal on Control and Optimization (2025). [ArXiv] [Article]
Comparison of Viscosity Solutions for a Class of Second Order PDEs on the Wasserstein Space, with Erhan Bayraktar and Ibrahim Ekren, Communications in Partial Differential Equations (2025). [ArXiv] [Article]
k-core in Percolated Dense Graph Sequences, with Erhan Bayraktar and Suman Chakraborty, Journal of Applied Probability (2025). [ArXiv] [Article]
Stability and Sample Complexity of Divergence Regularized Optimal Tranposrt, with Erhan Bayraktar and Stephan Eckstein, Bernoulli (2025). [ArXiv] [Article]
A PDE Approach for Regret Bounds under Partial Monitoring, with Erhan Bayraktar and Ibrahim Ekren, Journal of Machine Learning Research (2023). [ArXiv] [Article]
Propagation of Chaos of Forward-Backward Stochastic Differential Equations with Graphon Interactions, with Erhan Bayraktar and Ruoyu Wu, Applied Mathematics and Optimization (2023). [ArXiv] [Article]
A Smooth Variational Principle on Wasserstein Space, with Erhan Bayraktar and Ibrahim Ekren, Proceedings of the American Mathematical Society (2023). [ArXiv] [Article]
Dynamic Cournot-Nash Equilibrium: the Non-Potential Case, with Julio Backhoff, Mathematics and Financial Economics (2023). [ArXiv] [Article]
Solvability of Infinite Horizon McKean-Vlasov FBSDEs in Mean Field Control Problems and Games, with Erhan Bayraktar, Applied Mathematics and Optimization (2023). [ArXiv] [Article]
Prediction Against a Limited Adversary, with Erhan Bayraktar and Ibrahim Ekren, Journal of Machine Learning Research (2021). [ArXiv] [Article]
Embedding of Walsh Brownian Motion, with Erhan Bayraktar, Stochastic Processes and their Applications (2021). [ArXiv] [Article]
Malicious Experts Versus the Multiplicative Weights Algorithm in Online Prediction, with Erhan Bayraktar and H. Vincent Poor, IEEE Transactions on Information Theory (2021). [ArXiv] [Article]
Transport Plans with Domain Constraints, with Erhan Bayraktar and Zhou Zhou, Applied Mathematics and Optimization (2021). [ArXiv] [Article]
On Non-uniqueness in Mean Field Games, with Erhan Bayraktar, Proceedings of the American Mathematical Society (2020). [ArXiv] [Article]
Finite-Time 4-Expert Prediction Problem, with Erhan Bayraktar and Ibrahim Ekren, Communications in Partial Differential Equations (2020). [ArXiv] [Article]

Co-authors: Daniel Bartl, Julio Backhoff, Erhan Bayraktar, Mathias Beiglböck, Suman Chakraborty, Yan Dolinsky, Stephan Eckstein, Ibrahim Ekren, Xihao He, Gudmund Pammer, H. Vincent Poor, Jinniao Qiu, Stefan Schrott, Ho Man Tai, Valentin Tissot-Daguette, Zhizhang Wang, Ruoyu Wu, Jingjie Zhang, Zhou Zhou.