Publications

Books

• J. Cvitanic and J. Zhang, Contract theory in continuous-time models, Springer Finance. Springer, Heidelberg, 2012. (Amazon, Springer).
• J. Zhang, Backward Stochastic Differential Equations — from linear to fully nonlinear theory, Springer, New York, 2017.(Amazon, Springer, Errata)

Papers

• J. Ma, G. Wang, J. Zhang, and X.Y. Zhou, Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence, preprint, arXiv:2609.14972.
• J. Li, J. Zhang and Z. Zhu, Stackelberg Games with a Robust Leader, preprint, arXiv:2607.21890.
• J. Sung, J. Zhang and Z. Zhu, A General Model for Continuous Time Principal-Agent Problem Under Hidden Action, preprint, arXiv:2607.17212.
• C. Mou, J. Zhang and J. Zhou, Local well-posedness of general mean field game master equations, preprint, arXiv:2606.29132.
• Z. Gu and J. Zhang, On Information Controls, preprint, arXiv:2602.07318.
• J. Ma, W. Xia and J. Zhang, Wealth or Stealth? The Camouflage Effect in Insider Trading, preprint, arXiv:2512.06309.
• J. Ma, W. Xia and J. Zhang, Characterizing Nonconvex Boundaries via Scalarization, preprint, arXiv:2510.09918.
• B. Qiao and J. Zhang, A New Approach for the Continuous Time Kyle-Back Strategic Insider Equilibrium Problem, preprint, arXiv:2506.12281.
• C. Mou, J. Zhang and J. Zhou, Second-order monotonicity conditions and mean field games with volatility control, preprint, arXiv:2503.10097.
• M. Soner, V. Tissot-Daguette, and J. Zhang, Controlled Occupied Processes and Viscosity Solutions, preprint, arXiv:2411.12080.
• A. Lazrak and J. Zhang, Unlocking Democratic Efficiency: How Coordinated Outcome-Contingent Promises Shape Decisions, preprint, arXiv:2304.08008.
• J. Zhou, N. Touzi, and J. Zhang, Viscosity Solutions for HJB Equations on the Process Space: Application to Mean Field Control with Common Noise, Journal of the European Mathematical Society, accepted,  arXiv:2401.04920.
• J. Zhang, Instability and Efficiency of Non-cooperative Games, Mathematical Finance, Special Issue in Honour of Prof. Xunyu Zhou, accepted, arXiv:2405.17196.
• M. Iseri and J. Zhang, Set Valued Hamilton-Jacobi-Bellman Equations, Annals of Probability, accepted, arXiv:2311.05727.
• J. Ma, G. Wang, and J. Zhang, Convergence Analysis for Entropy-Regularized Control Problems: a Probabilistic Approach, SIAM Journal on Control and Optimization, 64 (2026), 816-842.
• B. Qiao and J. Zhang, Set Values of Dynamic Nonzero Sum Games and Set Valued Hamiltonians, SIAM Journal on Control and Optimization, 64 (2026), 316-334.
• J. Zhang and Z. Zhu, A Dynamic Principal Agent Problem with One-sided Commitment, Mathematics of Operations Research, 50 (2025), 2600-2632.
• C. Mou and J. Zhang, Mean Field Game Master Equations with Anti-monotonicity Conditions, Journal of the European Mathematical Society, 27 (2025), 4469-4499.
• 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 Erratum)
• 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 Erratum)
• 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).