Books

Papers

  • M. Soner, V. Tissot-Daguette, and J. Zhang, Controlled Occupied Processes and Viscosity Solutions, preprint, arXiv:2411.12080.
  • B. Qiao and J. Zhang, Set Values of Dynamic Nonzero Sum Games and Set Valued Hamiltonians, preprint, arXiv:2408.09047.
  • J. Ma, G. Wang, and J. Zhang, On Convergence Analysis of Policy Iteration Algorithms for Entropy-Regularized Stochastic Control Problems, preprint, arXiv:2406.10959.
  • J. Zhang, Instability and Efficiency of Non-cooperative Games, preprint, arXiv:2405.17196.
  • J. Zhou, N. Touzi, and J. Zhang, Viscosity Solutions for HJB Equations on the Process Space: Application to Mean Field Control with Common Noise, preprint, arXiv:2401.04920.
  • M. Iseri and J. Zhang, Set Valued Hamilton-Jacobi-Bellman Equations, preprint, arXiv:2311.05727.
  • A. Lazrak and J. Zhang, Democratic Policy Decisions with Decentralized Promises Contingent on Vote Outcome, preprint, arXiv:2304.08008.
  • J. Zhang and Z. Zhu, A Dynamic Principal Agent Problem with One-sided Commitment, Mathematics of Operations Research, accepted, arXiv:2208.06473.
  • C. Mou and J. Zhang, Mean Field Game Master Equations with Anti-monotonicity Conditions, Journal of the European Mathematical Society, accepted, arXiv:2201.10762.
  • M. Iseri and J. Zhang, Set Values for Mean Field Games, Transactions of the AMS,  377 (2024), 7117-7174.
  • C. Mou and J. Zhang, Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data, Memoirs of the AMS, 302(2024), no. 1515.
  • M. Talbi, N. Touzi, and J. Zhang, From finite population optimal stopping to mean field optimal stopping, Annals of Applied Probability, 34(2024),  4237-4267.
  • C. Mou and J. Zhang, Minimal Solutions of Master Equations for Extended Mean Field Games, Journal des Mathématiques Pures et Appliquées, 184(2024), 190-217.
  • J. Zhang, Is a sophisticated agent always a wise one? SIAM Journal on Financial Mathematics Short Communications, 14(2023), SC42-SC48.
  • Q. Feng and J. Zhang, Cubature Method for Stochastic Volterra Integral Equations, SIAM Journal on Financial Mathematics, 14(2023), 959-1003.
  • S. Yao and J. Zhang,  Preface: A Tribute to Professor Jin Ma on His 65th Birthday, Numerical Algebra, Control and Optimization, 13 (3\&4), 2023, pp. i-ii, doi:10.3934/naco.202303i.
  • M. Talbi, N. Touzi, and J. Zhang, Dynamic Programming Equation for the Mean Field Optimal Stopping Problem, SIAM Journal on Control and Optimization, 61 (2023),  2140-2164.
  • M. Talbi, N. Touzi, and J. Zhang, Viscosity Solutions for Obstacle Problems on Wasserstein Space, SIAM Journal on Control and Optimization, 61 (2023), 1712-1736.
  • W. Gangbo, A. Meszaros, C. Mou, and J. Zhang, Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity, Annals of Probability, 50 (2022), 2178-2217.
  • C. Mou and J. Zhang, Mean Field Games of Controls: Propagation of Monotonicities, Probability, Uncertainty and Quantitative Risk, 7 (2022), 247-274.
  • H. Wang, J. Yong, and J. Zhang, Path Dependent Feynman-Kac Formual for Forward Backward Stochastic Volterra Integral Equations, Annales de l’Institut Henri Poincare, 58 (2022), 603-638.
  • Z. Feinstein, B. Rudloff, and J. Zhang, Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums, Mathematics of Operations Research, 47 (2022), 616-642.
  • J. Ma, T.K. L. Wong and J. Zhang, Time-consistent Conditional Expectation under Probability Distortion, Mathematics of Operations Research, 46 (2021), 1149-1180.
  • J. Yong and J. Zhang, Non-Equivalence of Stochastic Optimal Control Problems with Open and Closed Loop Controls, Systems and Control Letters, 153 (2021), 104948.
  • R. Buckdahn, C. Keller, J. Ma and J. Zhang, Fully Nonlinear Stochastic and Rough PDEs: Classical and Viscosity Solutions, Probability, Uncertainty and Quantitative Risk, (2020) 5:7, DOI: 10.1186/s41546-020-00049-8.
  • D. Possamai, N. Touzi and J. Zhang, Zero-sum Path-dependent Stochastic Differential Games in Weak Formulation, Annals of Applied Probability, 30 (2020), 1415-1457.
  • C. Wu and J. Zhang, An Elementary Proof for the Structure of Wasserstein Derivatives, unpublished note.
  • C. Wu and J. Zhang, Viscosity Solutions to Parabolic Master Equations and McKean-Vlasov SDEs with Closed-loop Controls, Annals of Applied Probability, 30 (2020), 936-986.
  • Z. Ren, N. Touzi and J. Zhang , Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs, SIAM Journal on Control and Optimization, 58 (2020), 277-302.
  • F. Viens and J. Zhang, A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs , Annals of Applied Probability, 29 (2019), 3489-3540.
  • Y. Saporito and J. Zhang, Stochastic Control with Delayed Information and Related Nonlinear Master Equation , SIAM Journal on Control and Optimization, 57 (2019), 693-717.
  • H. Wang and J. Zhang, Forward Backward SDEs in Weak Formulation, Mathemtical Control and Related Fields, 8 (2018), 1021-1049.
  • C. Karnam, J. Ma and J. Zhang , Dynamic Approaches for Some Time Inconsistent Optimization Problems, Annals of Applied Probability, 27 (2017), 3435-3477.
  • Z. Ren, N. Touzi and J. Zhang , Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs, SIAM Journal on Mathematical Analysis, 49 (2017), 4093-4116.
  • J. Diehl and J. Zhang , Backward Stochastic Differential Equations with Young Drift, Probability, Uncertainty and Quantitative Risk, (2017) 2:5 DOI 10.1186/s41546-017.
  • I. Ekren and J. Zhang , Pseudo-Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs, Probability, Uncertainty and Quantitative Risk, (2016) 1:6, DOI 10.1186/s41546-016-0010-3.
  • J. Ma, Z. Ren, N. Touzi and J. Zhang , Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation , Annales de l’Institut Henri Poincare, 52 (2016), 1196-121.
  • I.Ekren, N. Touzi and J. Zhang , Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part II, Annals of Probability, 44 (2016), 2507-2553.
  • I. Ekren, N. Touzi and J. Zhang , Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part I, Annals of Probability, 44 (2016), 1212-1253.
  • C. Keller and J. Zhang , Pathwise Ito Calculus for Rough Paths and Rough PDEs with Path Dependent Coefficients, Stochastic Processes and Their Applications, 126 (2016), 735-766.
  • J. Ma, X. Wang and J. Zhang, Dynamic Equilibrium Limit Order Book Model and Optimal Execution Problem , Mathematical Control and Related Fields, 5 (2015), 557-583.
  • M. Nutz and J. Zhang, Optimal Stopping under Adverse Nonlinear Expectation and Related Games , Annals of Applied Probability, 25 (2015), 2503-2534.
  • J. Ma, Z. Wu, D. Zhang and J. Zhang, On Wellposedness of Forward-Backward SDEs — A Unified Approach, Annals of Applied Probability, 25 (2015), 2168-2214.
  • R. Buckdahn, J. Ma and J. Zhang, Pathwise Taylor Expansions for Random Fields on Multiple Dimensional Paths , Stochastic Processes and Their Applications, 125 (2015), 2820-2855.
  • W. Guo, J. Zhang and J. Zhuo, A Monotone Scheme for High Dimensional Fully Nonlinear PDEs, Annals of Applied Probability, 25 (2015), 1540-1580.
  • Z. Ren, N. Touzi and J. Zhang , An Overview of Viscosity Solutions of Path Dependent PDEs, Stochastic Analysis and Applications, 2014, 100 (2014), 397-453.
  • I. Ekren, N. Touzi and J. Zhang , Optimal Stopping under Nonlinear Expectation, Stochastic Processes and Their Applications, 124 (2014), 3277-3311.
  • S. Peng, Y. Song and J. Zhang, A Complete Representation Theorem for G-martingales, Stochastics, 86 (2014), 609-631.
  • T. Pham and J. Zhang, Two Person Zero-sum Game in Weak Formulation and Path Dependent Bellman-Isaacs Equation, SIAM Journal on Control and Optimization, 52 (2014), 2090-2121. (An Errata)
  • J. Zhang and J. Zhuo, Monotone Schemes for Fully Nonlinear Parabolic Path Dependent PDEs , Journal of Financial Engineering, 1 (2014) 1450005 (23 pages); DOI: 10.1142/S2345768614500056.
  • I. Ekren, C. Keller, N. Touzi and J. Zhang , On Viscosity Solutions of Path Dependent PDEs, Annals of Probability, 42 (2014), 204-236.
  • T. Pham and J. Zhang, Some Norm Estimates for Semimartingales, Electronic Journal of Probability, 18 (2013), no. 109, 1-25. (An Errata)
  • J. Ma, Q. Song, J. Xu, and J. Zhang, Optimal Portfolio Selection under Concave Price Impact, Applied Mathematics and Optimization, 67 (2013), 353-390.
  • M. Soner, N. Touzi and J. Zhang , Dual formulation of the second order target problems, Annals of Applied Probability, 23 (2013), 308-347.
  • J. Ma, H. Yin and J. Zhang, On Non-Markovian Forward Backward SDEs and Backward Stochastic PDEs, Stochastic Processes and Their Applications, 122 (2012), no. 12, 3980-4004.
  • J. Cvitanic, J. Ma and J. Zhang , Law of Large Numbers for Self-Exciting Correlated Defaults, Stochastic Processes and Their Applications, 122 (2012), 2781 – 2810.
  • M. Soner, N. Touzi and J. Zhang, Wellposedness of Second Order Backward SDEs, Probability Theory and Related Fields, 153 (2012), 149-190.
  • J. Ma and J. Zhang, On weak solutions of FBSDEs, Probability Theory and Related Fields, 151 (2011), 475-507.
  • M. Soner, N. Touzi and J. Zhang, Quasi-sure Stochastic Analysis through Aggregation, Electronic Journal of Probability, 16 (2011), 1844-1879.
  • M. Soner, N. Touzi and J. Zhang, , Martingale representation theorem for the G-expectation, Stochastic Processes and Their Applications, 121 (2) (2011), 265-287.
  • I. Kharroubi, J. Ma, H. Pham, and J. Zhang, Backward SDEs with constrained jumps and Quasi-Variational Inequalities, Annals of Probability, 38 (2), (2010), 794-840.
  • S. Hamadene and J. Zhang, The continuous time nonzero-sum Dynkin game problem and application in game options, SIAM Journal on Control and Optimization, 48 (5), (2010), 3659-3669.
  • S. Hamadene and J. Zhang, Switching problem and related system of reflected BSDEs, Stochastic Processes and Their Applications, 120 (4), (2010), 403-426.
  • J. Cvitanic, X. Wan and J. Zhang, Continuous-Time Principal-Agent Problems with Hidden Action and Lump-Sum Payment, Applied Mathematics and Optimization, 59 (1) (2009), 99-146.
  • J. Ma, J. Zhang and Z. Zheng, Weak Solutions for Forward-Backward SDEs— A Martingale Problem Approach, Annals of Probability, 36 (6) (2008), 2092-2125.
  • J. Cvitanic, X. Wan, and J. Zhang, Principal agent problems with exit options, B.E. Journal of Theoretical Economics, 8 (1) (Contributions) (2008), Article 23.
  • C. Bender and J. Zhang, Time Discretization and Markovian Iteration for Coupled FBSDEs, Annals of Applied Probability, 18 (1) (2008), 143-177.
  • J. Cvitanic and J. Zhang, Optimal Compensation with Adverse Selection and Dynamic Actions, Mathematics and Financial Economics, 1 (1) (2007), 21-55.
  • J. Cvitanic, X. Wan and J. Zhang, Optimal contracts in continuous-time models, Journal of Applied Mathematics and Stochastic Analysis, Volume 2006 (2006), Article ID 95203.
  • J. Zhang, Rate of Convergence of Finite Difference Approximations for Degenerate ODEs, Mathematics of Computation, 75 (256) (2006), 1755-1778.
  • J. Zhang, The Wellposedness of FBSDEs (II), unpublished note.
  • J. Zhang, The Wellposedness of FBSDEs, Discrete and Continuous Dynamical Systems-Series B, 6 (2006), 927-940.
  • J. Cvitanic and J. Zhang, The Steepest Descent Method for FBSDEs, Electronic Journal of Probability, 10 (2005), 1468-1495.
  • J. Zhang, Representation of Solutions to BSDEs Associated with a Degenerate FSDE, Annals of Applied Probability, 15 (2005), 1798-1831.
  • J. Ma and J. Zhang, Representations and regularities for solutions to backward stochastic differential equations with reflections, Stochastic Processes and Their Applications, 115 (2005), 539-569.
  • J. Zhang, A numerical scheme for backward stochastic differential equations, Annals of Applied Probability, 14 (2004), 459-488.
  • J. Cvitanic, J. Ma, and J. Zhang, Efficient computation of delta-hedges for options with discontinuous payoffs, Mathematical Finance, 13 (2003), 135-151.
  • J. Ma and J. Zhang, Representation theorems for backward stochastic differential equations, Annals of Applied Probability, 12 (2002), 1390-1418.
  • J. Ma and J. Zhang, Path regularity of solutions to backward stochastic differential equations, Probability Theory and Related Fields, 122 (2002), 163-190.
  • J. Ma, P. Protter, and J. Zhang, Explicit form and path regularity of martingale representations, Levy Processes – Theory and Applications, O.E.Barndorff-Nielsen, T. Mikosch and S.I. Resnick (Eds.), Birkhauser Boston,(2001), 337-360.

PhD Thesis

  • J. Zhang, Some fine properties of backward stochastic differential equations, with applications, Ph.D. dissertation, Purdue University, (2001).