Publications

 [38] Error Estimates of Physics-Informed Neural Networks for Approximating Boltzmann Equation (with E. Abdo, L. Chai, X. Yang)
          Submitted, arXiv:2407.08383. [arXiv]

 [37] Finite-Agent Stochastic Differential Games on Large Graphs: I. The Linear-Quadratic Case (with J. Long, H. Zhou)
  Submitted, arXiv:2406.09523. [arXiv]

 [36] On the Three-dimensional Nernst-Planck-Boussinesq System (with E. Abdo, Q. Lin)
          Submitted, arXiv:2405.02152. [arXiv]

 [35] Multi-Agent Relative Investment Games in a Jump Diffusion Market with Deep Reinforcement Learning Algorithm (with L. Lu, X. Yang, Y. Zhu)
          Submitted, arXiv:2404.11967. [arXiv]

 [34] A PDE Perspective on Approximating Nonlocal Periodic Operators with Applications on Neural Networks for Critical SQG Equations (with E. Abdo, Q. Lin)
         Submitted. [article]

 [33] On the Long-time Dynamics and Ergodicity of the Stochastic Nernst-Planck-Navier-Stokes System (with E. Abdo, Q. Lin)
          Submitted, arXiv: 2310.20484. [arXiv]

 [32] A Deep Learning Analysis of Climate Change, Innovation, and Uncertainty (with M. Barnett, W. Brock, L. Hansen, J. Huang)
          Working paper, arXiv:2310.13200. [arXiv]

 [31] Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spaces (with A. Angiuli, J.-P. Fouque, A. Raydan)
          Submitted, arXiv:2309.10953. [arXiv]

 [30] Anisotropic Viscosities Estimation for the Stochastic Primitive Equations (with I. Cialenco, Q. Lin)
          Submitted, arXiv:2309.06952. [arXiv]

 [29] Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms (with R. Balkin, H. Ceniceros)
          Journal of Machine Learning, 3(1), 23-63, 2024. [arXiv] [Journal]

 [28] Directed Chain Generative Adversarial Networks (with M. Min, T. Ichiba)
          International Conference on Machine Learning (ICML), PMLR 202:24812-24830, 2023. [arXiv] [Proceedings]
                  -  Invited talk at AAAI-2023 Workshop on Multimodal AI for Financial Forecasting

 [27] Pathwise Solutions for Stochastic Hydrostatic Euler Equations and Hydrostatic Navier-Stokes Equations Under the Local Rayleigh Condition (with Q. Lin)
          Submitted, arXiv:2301.07810. [arXiv]

 [26] Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems (with C. Gao, S. Gao, Z. Zhu)
          SIAM Journal on Financial Mathematics, 14(4):1290-1303, 2023. [arXiv] [Journal]

 [25] Higher-Order Error Estimates for Physics-Informed Neural Networks Approximating the Primitive Equations (with Q. Lin, A. Raydan, S. Tang)
          Partial Differential Equations and Applications, 4(4):34, 2023. [arXiv] [Journal]

 [24] Discussion on "Programmable money: next generation blockchain based conditional payments" by Ingo Weber and Mark Staples (with A. M. Rodrigues)
          Digital Finance, 4(2), 141-142, 2022. [Journal]

 [23] Pandemic Control, Game Theory and Machine Learning (with Y. Xuan, R. Balkin, J. Han, H. Ceniceros)
          Notices of the AMS, 69(11), 1878-1887, December 2022. [arXiv] [Notices]

 [22] Recent Developments in Machine Learning Methods for Stochastic Control and Games (with M. Lauriere).
          Numerical Algebra, Control and Optimization, accepted, [SSRN] [arXiv]. Tutorial video at the Fields Institute Bootcamp [Tutorial]. 

 [21] Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence (with J. Han, J. Long)
          SIAM Journal on Numerical Analysis, 62(1), 1-24, 2024. [arXiv] [Journal]   

 [20] Systemic Risk Models for Disjoint and Overlapping Groups with Equilibrium Strategies (with Y. Feng, J.-P. Fouque, T. Ichiba)
          Statistics & Risk Modeling, 40(1-2), 21-51, 2023. [arXiv] [Journal]

 [19] Local Martingale Solutions and Pathwise Uniqueness for the Three-dimensional Stochastic Inviscid Primitive Equations (with Q. Lin)
          Stochastics and Partial Differential Equations: Analysis and Computations, 11(4), 1470-1518, 2023. [arXiv] [Journal]         

 [18] Sub- and Super-solution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Market (with J.-P. Fouque, R. Sircar)

         SIAM Journal on Financial Mathematics, 13(1), 109-128, 2022. [arXiv] [Journal]

 [17] N-player and Mean-field Games in It0-diffusion Markets with Competitive or Homophilous Interaction (with T. Zariphopoulou)

         Stochastic Analysis, Filtering, and Stochastic Optimization (Ed. G. Yin and T. Zariphopoulou), 209-237, 2022. [arXiv] [Book Chapter]

 [16] Signatured Deep Fictitious Play for Mean Field Games with Common Noise (with M. Min)

         Proceedings of the 38th International Conference on Machine Learning (ICML), PMLR 139:7736-7747, 2021. [arXiv] [Proceedings]

 [15] A Class of Dimension-free Metrics for the Convergence of Empirical Measures (with J. Han, J. Long)

         Stochastic Processes and their Applications, 164:242-287, 2023. [arXiv] [Journal]

 [14] Recurrent Neural Networks for Stochastic Control Problems with Delay (with J. Han)

         Mathematics of Control, Signals, and Systems, 33(4), 775-795, 2021. [arXiv] [Journal]

 [13] Optimal Policies for a Pandemic: A Stochastic Game Approach and a Deep Learning Algorithm (with Y. Xuan, R. Balkin, J. Han, H. Ceniceros)

         Mathematical and Scientific Machine Learning Conference (MSML2021), PMLR 145:987-1012, 2022. [arXiv] [Proceedings]

 [12] Convergence of Deep Fictitious Play for Stochastic Differential Games (with J. Han, J. Long)

         Frontiers of Mathematical Finance, 1(2), 287-319, 2022. [arXiv] [Journal]

 [11] Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-agent Games (with J. Han)

         Mathematical and Scientific Machine Learning Conference (MSML2020), 221-245, PMLR, 2020. [arXiv] [Proceedings]

 [10] Deep Fictitious Play for Stochastic Differential Games

         Communications in Mathematical Sciences, 19(2), 325-353, 2021. [arXiv] [Journal]

 [9] Multiscale Asymptotic Analysis for Portfolio Optimization under Stochastic Environment (with J.-P. Fouque)

        SIAM Journal on Multiscale Modeling and Simulation, 18(3), 1318-1342, 2020. [arXiv] [Journal]

 [8] Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems

        Quantitative Finance, 20(9), 1567-1581, 2020. [arXiv] [Journal]

 [7] Portfolio Optimization under Fast Mean-Reverting and Rough Fractional Stochastic Environment (with J.-P. Fouque)

       Applied Mathematical Finance, 25(4), 361-388, 2018. [arXiv] [Journal]

 [6] Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic Environments

       Proceedings of the 2018 IEEE Conference on Decision and Control (CDC), 5771-5776, 2018. [arXiv] [Journal]

 [5] Optimal Portfolio under Fast Mean-Reverting Fractional Stochastic Environment (with J.-P. Fouque) 

       SIAM Journal on Financial Mathematics, 6(2), 564-601, 2018. [arXiv] [Journal]

 [4] Optimal Portfolio under Fractional Stochastic Environment (with J.-P. Fouque)

       Mathematical Finance, Version of Record online: 20 Sept. 2018, DOI: 10.1111/mafi.12195. [arXiv] [Journal]

 [3] Systemic Risk and Optimal Fee Structure for Central Clearing Counterparty under Partial Netting (with Z. Cui, Q. Feng, and B. Zou)

       Operations Reseach Letters, 46(3), 306-311, 2018. [SSRN] [Journal]

 [2] Asymptotic Methods for Portfolio Optimization in a Slowly Varying Stochastic Environment (with J.-P. Fouque)

       SIAM Journal on Control and Optimization, 55(3), 1990--2023, 2017. [arXiv] [Journal]

 [1] Sequential Design for Ranking Response Surfaces (with M. Ludkovski) 

       SIAM/ASA Journal on Uncertainty Quantification, 5(1), 212--239, 2017. [arXiv] [Journal]