Hello everyone, I am Xin Zhang, now a university assistant in the group of Mathias Beiglböck at the University of Vienna. I obtained my Ph.D. in Mathematics under the supervision of 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 xin.zhang@univie.ac.at. 

Preprints and Publications (see also Google Scholar)

• Specific Wasserstein Divergence between Continuous Martingales, with Julio Backhoff. [ArXiv]

• Representing General Stochastic Processes as Martingale Laws, with Mathias Beiglböck, Gudmund Pammer, Stefan Schrott. [ArXiv]

• Comparison of Viscosity Solutions for a Class of Second Order PDEs on the Wasserstein Space, with Erhan Bayraktar and Ibrahim Ekren. [ArXiv]

• Walsh Diffusions as Time Changed Multi-parameter Processes, with Erhan Bayraktar and Jingjie Zhang. [ArXiv]

• k-core in Percolated Dense Graph Sequences, with Erhan Bayraktar and Suman Chakraborty. [ArXiv]

• Stability and Sample Complexity of Divergence Regularized Optimal Tranposrt, with Erhan Bayraktar and Stephan Eckstein, to appear in Bernoulli. [ArXiv]

• A PDE Approach for Regret Bounds under Partial Monitoring, with Erhan Bayraktar and Ibrahim Ekren, Journal of Machine Learning Research, Vol. 24, No. 299, 1-24, 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, Vol. 88, No. 1, 1-44, 2023. [ArXiv] [Article]

• A Smooth Variational Principle on Wasserstein Space, with Erhan Bayraktar and Ibrahim Ekren, Proceedings of the American Mathematical Society, Vol. 151, 4089-4098, 2023.  [ArXiv] [Article]

• Dynamic Cournot-Nash Equilibrium: the Non-Potential Case, with Julio Backhoff, Mathematics and Financial Economics, Vol. 17. No. 2, 153-174, 2023. [ArXiv] [Article]

• Solvability of Infinite Horizon McKean-Vlasov FBSDEs in Mean Field Control Problems and Games, with Erhan Bayraktar, Applied Mathematics and Optimization, Vol. 87, No. 13, 1-26, 2023. [ArXiv] [Article]

• Prediction Against a Limited Adversary, with Erhan Bayraktar and Ibrahim Ekren, Journal of Machine Learning Research, Vol. 22, No. 72, 1-33, 2021. [ArXiv] [Article]

• Embedding of Walsh Brownian Motion, with Erhan Bayraktar, Stochastic Processes and their Applications, Vol. 134, 1-28, 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, Vol. 67, No. 1, 559-565, 2021. [ArXiv] [Article]

• Transport Plans with Domain Constraints, with Erhan Bayraktar and Zhou Zhou,  Applied Mathematics and Optimization, Vol. 84, No. 1, 1131-1158, 2021. [ArXiv] [Article]

• On Non-uniqueness in Mean Field Games, with Erhan Bayraktar, Proceedings of the American Mathematical Society, Vol. 148, No. 9, 4091-4106, 2020. [ArXiv] [Article]

• Finite-Time 4-Expert Prediction Problem, with Erhan Bayraktar and Ibrahim Ekren, Communications in Partial Differential Equations, Vol. 45, No. 7, 714–757, 2020. [ArXiv] [Article]

Co-authors: Julio Backhoff, Erhan Bayraktar, Mathias Beiglböck, Suman Chakraborty, Stephan Eckstein, Ibrahim Ekren, Gudmund Pammer, Stefan Schrott, H. Vincent Poor, Ruoyu Wu, Jingjie Zhang, Zhou Zhou.