{"id":353,"date":"2023-06-14T13:59:52","date_gmt":"2023-06-14T20:59:52","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/jianfeng-zhang\/?page_id=353"},"modified":"2026-10-04T09:04:44","modified_gmt":"2026-10-04T16:04:44","slug":"publications","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <h2>Books<\/h2>\n<ul>\n<li>J. Cvitanic and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/book1.pdf\" target=\"_blank\" rel=\"noopener\"><i>Contract theory in continuous-time models<\/i><\/a>, Springer Finance. Springer, Heidelberg, 2012. (<a href=\"https:\/\/www.amazon.com\/Contract-Theory-Continuous-Time-Springer-Finance\/dp\/3642141994\">Amazon<\/a>, <a href=\"https:\/\/link.springer.com\/book\/10.1007%2F978-3-642-14200-0\">Springer<\/a>).<\/li>\n<li>J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/book2.pdf\" target=\"_blank\" rel=\"noopener\"><i>Backward Stochastic Differential Equations &#8212; from linear to fully nonlinear theory<\/i><\/a>, Springer, New York, 2017.(<a href=\"https:\/\/www.amazon.com\/Backward-Stochastic-Differential-Equations-Probability\/dp\/1493972545\">Amazon<\/a>, <a href=\"https:\/\/link.springer.com\/book\/10.1007\/978-1-4939-7256-2\">Springer<\/a>, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/book2_errata.pdf\">Errata<\/a>)<\/li>\n<\/ul>\n<h2>Papers<\/h2>\n<ul>\n<li>J. Ma, G. Wang, J. Zhang, and X.Y. Zhou, <em><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/09\/MWZZ-learning.pdf\" target=\"_blank\" rel=\"noopener\">Learning to Solve Stochastic Controls with Unknown Drifts and Running Rewards: Theory, Algorithms and Convergence<\/a>, <\/em>preprint, arXiv:2609.14972.<\/li>\n<li>J. Li, J. Zhang and Z. Zhu, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/07\/LZZ.pdf\" target=\"_blank\" rel=\"noopener\"><em><em><i>Stackelberg Games with a Robust Leader<\/i><\/em><\/em><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2607.21890.<\/li>\n<li>J. Sung, J. Zhang and Z. Zhu, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/07\/SZZ.pdf\" target=\"_blank\" rel=\"noopener\"><em>A General Model for Continuous Time Principal-Agent Problem Under Hidden Action<\/em><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2607.17212.<\/li>\n<li>C. Mou, J. Zhang and J. Zhou, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/09\/MZZ-local.pdf\" target=\"_blank\" rel=\"noopener\"><em><em>Local well-posedness of general mean field game master equations<\/em><\/em><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2606.29132.<\/li>\n<li>Z. Gu and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/03\/GZ-information.pdf\" target=\"_blank\" rel=\"noopener\"><i><i>On Information Controls<\/i><\/i><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2602.07318.<\/li>\n<li>J. Ma, W. Xia and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/12\/MXZ-insider.pdf\" target=\"_blank\" rel=\"noopener\"><i><i>Wealth or Stealth? The Camouflage Effect in Insider Trading<\/i><\/i><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2512.06309.<\/li>\n<li>J. Ma, W. Xia and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/10\/MXZ-nonconvex.pdf\" target=\"_blank\" rel=\"noopener\"><i>Characterizing Nonconvex Boundaries via Scalarization<\/i><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2510.09918.<\/li>\n<li>B. Qiao and J. Zhang,\u00a0<a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/06\/QZ-Insider.pdf\" target=\"_blank\" rel=\"noopener\"><i>A New Approach for the Continuous Time <i>Kyle-Back Strategic Insider Equilibrium Problem<\/i><\/i><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2506.12281.<\/li>\n<li>C. Mou, J. Zhang and J. Zhou, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/03\/MZZ-Volatility.pdf\" target=\"_blank\" rel=\"noopener\"><em><em>Second-order monotonicity conditions and mean field games with volatility control<\/em><\/em><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2503.10097.<\/li>\n<li>M. Soner, V. Tissot-Daguette, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2024\/11\/STZ-Occupied.pdf\" target=\"_blank\" rel=\"noopener\"><em>Controlled Occupied Processes and Viscosity Solutions<\/em><\/a><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2411.12080.<\/li>\n<li>A. Lazrak and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/LZ-voting.pdf\" target=\"_blank\" rel=\"noopener\"><i>Unlocking Democratic Efficiency: How Coordinated <i>Outcome-Contingent Promises Shape Decisions<\/i><\/i><\/a>, preprint, arXiv:2304.08008.<\/li>\n<li>J. Zhou, N. Touzi, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/TZZ.pdf\" target=\"_blank\" rel=\"noopener\"><em><em><em>Viscosity Solutions for HJB Equations on the Process Space: Application to Mean Field Control with Common Noise<\/em><\/em><\/em><\/a><em><em>, <\/em><\/em>Journal of the European Mathematical Society, accepted, \u00a0arXiv:2401.04920.<\/li>\n<li>J. Zhang, <em><em><em>I<a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/Efficiency.pdf\" target=\"_blank\" rel=\"noopener\">nstability and Efficiency of Non-cooperative Games<\/a><\/em><\/em><\/em><em><em>, <\/em><\/em>Mathematical Finance, Special Issue in Honour of Prof. Xunyu Zhou, accepted, arXiv:2405.17196.<\/li>\n<li>M. Iseri and J. Zhang, <em><em><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/IZ-SVHJB.pdf\" target=\"_blank\" rel=\"noopener\">Set Valued Hamilton-Jacobi-Bellman Equations<\/a>, <\/em><\/em>Annals of Probability, accepted, arXiv:2311.05727.<\/li>\n<li>J. Ma, G. Wang, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/04\/MWZ-PIA.pdf\" target=\"_blank\" rel=\"noopener\"><i>Convergence Analysis<\/i><i> for Entropy-Regularized <i>Control Problems: a Probabilistic Approach<\/i><\/i><\/a><em><em>, <\/em><\/em>SIAM Journal on Control and Optimization, 64 (2026), 816-842.<\/li>\n<li>B. Qiao and J. Zhang,\u00a0<i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/01\/QZ-Hamiltonian.pdf\" target=\"_blank\" rel=\"noopener\">Set Values of Dynamic Nonzero Sum Games and Set Valued Hamiltonians<\/a><i>,<\/i><\/i> SIAM Journal on Control and Optimization, 64 (2026), 316-334.<\/li>\n<li>J. Zhang and Z. Zhu, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/11\/ZZ-PA.pdf\" target=\"_blank\" rel=\"noopener\"><em>A Dynamic Principal Agent Problem with One-sided Commitment<\/em><\/a>, Mathematics of Operations Research, 50 (2025), 2600-2632.<\/li>\n<li>C. Mou and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/09\/MZ-anti.pdf\" target=\"_blank\" rel=\"noopener\"><em>Mean Field Game Master Equations with Anti-monotonicity Conditions<\/em><\/a>, Journal of the European Mathematical Society, 27 (2025), 4469-4499.<\/li>\n<li>M. Iseri and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/01\/Iseri-Zhang.pdf\" target=\"_blank\" rel=\"noopener\"><em>Set Values for Mean Field Games<\/em><\/a>, Transactions of the AMS, \u00a0377 (2024), 7117-7174.<\/li>\n<li>C. Mou and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/MZ-Master.pdf\" target=\"_blank\" rel=\"noopener\"><em>Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data<\/em><\/a>, Memoirs of the AMS, 302(2024), no. 1515.<\/li>\n<li>M. Talbi, N. Touzi, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2024\/10\/TTZ3.pdf\" target=\"_blank\" rel=\"noopener\"><i>From finite population optimal stopping to mean field optimal stopping<\/i><\/a>, Annals of Applied Probability, 34(2024), \u00a04237-4267.<\/li>\n<li>C. Mou and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2024\/05\/MZ-EMFG.pdf\" target=\"_blank\" rel=\"noopener\"><em>Minimal Solutions of Master Equations for Extended Mean Field Games<\/em><\/a>, Journal des Math\u00e9matiques Pures et Appliqu\u00e9es, 184(2024), 190-217.<\/li>\n<li>J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/11\/InconsistentExample.pdf\" target=\"_blank\" rel=\"noopener\"><i>Is a sophisticated agent always a wise one? <\/i><\/a>SIAM Journal on Financial Mathematics Short Communications, 14(2023), SC42-SC48.<\/li>\n<li>Q. Feng and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/11\/FZ-cubature.pdf\" target=\"_blank\" rel=\"noopener\"><em>Cubature Method for Stochastic Volterra Integral Equations<\/em><\/a>, SIAM Journal on Financial Mathematics, 14(2023), 959-1003.<\/li>\n<li>S. Yao and J. Zhang, <em><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/08\/YZ-JinPreface.pdf\" target=\"_blank\" rel=\"noopener\">Preface: A Tribute to Professor Jin Ma on His 65th Birthday<\/a><\/em>, Numerical Algebra, Control and Optimization, 13 (3\\&amp;4), 2023, <i>pp. i-ii, <\/i>doi:10.3934\/naco.202303i.<\/li>\n<li>M. Talbi, N. Touzi, and J. Zhang, <a href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/08\/TTZ.pdf\" target=\"_blank\" rel=\"noopener\"><em>Dynamic Programming Equation for the Mean Field Optimal Stopping Problem<\/em><\/a>, SIAM Journal on Control and Optimization, 61 (2023), <span class=\"\" data-v-3708431c=\"\">\u00a02140-2164.<\/span><\/li>\n<li>M. Talbi, N. Touzi, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/08\/TTZ2.pdf\" target=\"_blank\" rel=\"noopener\"><em>Viscosity Solutions for Obstacle Problems on Wasserstein Space<\/em><\/a>, SIAM Journal on Control and Optimization, 61 (2023), 1712-1736.<\/li>\n<li>W. Gangbo, A. Meszaros, C. Mou, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/GMMZ.pdf\" target=\"_blank\" rel=\"noopener\"><em>Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity<\/em><\/a>, Annals of Probability, 50 (2022), 2178-2217.<\/li>\n<li>C. Mou and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/MZ-MFGC.pdf\" target=\"_blank\" rel=\"noopener\"><em>Mean Field Games of Controls: Propagation of Monotonicities<\/em><\/a>, Probability, Uncertainty and Quantitative Risk, 7 (2022), 247-274.<\/li>\n<li>H. Wang, J. Yong, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/WYZ.pdf\" target=\"_blank\" rel=\"noopener\"><em>Path Dependent Feynman-Kac Formual for Forward Backward Stochastic Volterra Integral Equations<\/em><\/a>, Annales de l&#8217;Institut Henri Poincare, 58 (2022), 603-638.<\/li>\n<li>Z. Feinstein, B. Rudloff, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/FRZ.pdf\" target=\"_blank\" rel=\"noopener\"><em>Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums<\/em><\/a>, Mathematics of Operations Research, 47 (2022), 616-642.<\/li>\n<li>J. Ma, T.K. L. Wong and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/MWZ.pdf\" target=\"_blank\" rel=\"noopener\"><em>Time-consistent Conditional Expectation under Probability Distortion<\/em><\/a>, Mathematics of Operations Research, 46 (2021), 1149-1180.<\/li>\n<li>J. Yong and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/YZ-example.pdf\" target=\"_blank\" rel=\"noopener\"><em>Non-Equivalence of Stochastic Optimal Control Problems with Open and Closed Loop Controls<\/em><\/a>, Systems and Control Letters, 153 (2021), 104948.<\/li>\n<li>R. Buckdahn, C. Keller, J. Ma and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/BKMZ.pdf\" target=\"_blank\" rel=\"noopener\"><i>Fully Nonlinear Stochastic and Rough PDEs: Classical and Viscosity Solutions<\/i><\/a>, Probability, Uncertainty and Quantitative Risk, (2020) 5:7, DOI: 10.1186\/s41546-020-00049-8.<\/li>\n<li>D. Possamai, N. Touzi and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/PTZ.pdf\" target=\"_blank\" rel=\"noopener\"><i><em>Zero-sum Path-dependent Stochastic Differential Games in Weak Formulation<\/em><\/i><\/a>, Annals of Applied Probability, 30 (2020), 1415-1457.<\/li>\n<li>C. Wu and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/WZ-derivative.pdf\" target=\"_blank\" rel=\"noopener\"><i>An Elementary Proof for the Structure of Wasserstein Derivatives<\/i><\/a>, unpublished note.<\/li>\n<li>C. Wu and J. Zhang, <a href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/07\/WZ-master-1.pdf\" target=\"_blank\" rel=\"noopener\"><i>Viscosity Solutions to Parabolic Master Equations and McKean-Vlasov SDEs with Closed-loop Controls<\/i><\/a>, Annals of Applied Probability, 30 (2020), 936-986.<\/li>\n<li>Z. Ren, N. Touzi and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/RTZ-semilinear.pdf\" target=\"_blank\" rel=\"noopener\"><i>Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs<\/i><\/a>, SIAM Journal on Control and Optimization, 58 (2020), 277-302.<\/li>\n<li>F. Viens and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/VZ-fBM.pdf\" target=\"_blank\" rel=\"noopener\">A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs<\/a><\/i>, Annals of Applied Probability, 29 (2019), 3489-3540.<\/li>\n<li>Y. Saporito and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/SZ.pdf\" target=\"_blank\" rel=\"noopener\"><i>Stochastic Control with Delayed Information and Related Nonlinear Master Equation<\/i><\/a>, SIAM Journal on Control and Optimization, 57 (2019), 693-717.<\/li>\n<li>H. Wang and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/WZ-FBSDE.pdf\" target=\"_blank\" rel=\"noopener\"><i>Forward Backward SDEs in Weak Formulation<\/i><\/a>, Mathemtical Control and Related Fields, 8 (2018), 1021-1049.<\/li>\n<li>C. Karnam, J. Ma and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/48.pdf\" target=\"_blank\" rel=\"noopener\"><i>Dynamic Approaches for Some Time Inconsistent Optimization Problems<\/i><\/a>, Annals of Applied Probability, 27 (2017), 3435-3477.<\/li>\n<li>Z. Ren, N. Touzi and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/47.pdf\" target=\"_blank\" rel=\"noopener\"><i>Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs<\/i><\/a>, SIAM Journal on Mathematical Analysis, 49 (2017), 4093-4116.<\/li>\n<li>J. Diehl and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/46.pdf\" target=\"_blank\" rel=\"noopener\"><i>Backward Stochastic Differential Equations with Young Drift<\/i><\/a>, Probability, Uncertainty and Quantitative Risk, (2017) 2:5 DOI 10.1186\/s41546-017.<\/li>\n<li>I. Ekren and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/45.pdf\" target=\"_blank\" rel=\"noopener\"><i>Pseudo-Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs<\/i><\/a>, Probability, Uncertainty and Quantitative Risk, (2016) 1:6, DOI 10.1186\/s41546-016-0010-3.<\/li>\n<li>J. Ma, Z. Ren, N. Touzi and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/44.pdf\" target=\"_blank\" rel=\"noopener\"><i>Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation<\/i><\/a>, Annales de l&#8217;Institut Henri Poincare, 52 (2016), 1196-121<a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/43.pdf\">.<\/a><\/li>\n<li>I.Ekren, N. Touzi and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/43.pdf\" target=\"_blank\" rel=\"noopener\"><i>Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part II<\/i><\/a>, Annals of Probability, 44 (2016), 2507-2553.<\/li>\n<li>I. Ekren, N. Touzi and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/42.pdf\" target=\"_blank\" rel=\"noopener\"><i>Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part I<\/i>,<\/a> Annals of Probability, 44 (2016), 1212-1253.<\/li>\n<li>C. Keller and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/41.pdf\" target=\"_blank\" rel=\"noopener\"><i>Pathwise Ito Calculus for Rough Paths and Rough PDEs with Path Dependent Coefficients<\/i><\/a>, Stochastic Processes and Their Applications, 126 (2016), 735-766.<\/li>\n<li>J. Ma, X. Wang and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/40.pdf\" target=\"_blank\" rel=\"noopener\"><i>Dynamic Equilibrium Limit Order Book Model and Optimal Execution Problem<\/i><\/a>, Mathematical Control and Related Fields, 5 (2015), 557-583.<\/li>\n<li>M. Nutz and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/39.pdf\" target=\"_blank\" rel=\"noopener\"><i>Optimal Stopping under Adverse Nonlinear Expectation and Related Games<\/i><\/a>, Annals of Applied Probability, 25 (2015), 2503-2534.<\/li>\n<li>J. Ma, Z. Wu, D. Zhang and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/38.pdf\" target=\"_blank\" rel=\"noopener\"><i>On Wellposedness of Forward-Backward SDEs &#8212; A Unified Approach<\/i><\/a>, Annals of Applied Probability, 25 (2015), 2168-2214.<\/li>\n<li>R. Buckdahn, J. Ma and J. Zhang,<a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/37.pdf\" target=\"_blank\" rel=\"noopener\"> <i>Pathwise Taylor Expansions for Random Fields on Multiple Dimensional Paths<\/i><\/a>, Stochastic Processes and Their Applications, 125 (2015), 2820-2855.<\/li>\n<li>W. Guo, J. Zhang and J. Zhuo, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/36.pdf\" target=\"_blank\" rel=\"noopener\"><i>A Monotone Scheme for High Dimensional Fully Nonlinear PDEs<\/i><\/a>, Annals of Applied Probability, 25 (2015), 1540-1580.<\/li>\n<li>Z. Ren, N. Touzi and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/35.pdf\" target=\"_blank\" rel=\"noopener\"><i>An Overview of Viscosity Solutions of Path Dependent PDEs<\/i><\/a>, Stochastic Analysis and Applications, 2014, 100 (2014), 397-453.<\/li>\n<li>I. Ekren, N. Touzi and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/34.pdf\" target=\"_blank\" rel=\"noopener\"><i>Optimal Stopping under Nonlinear Expectation<\/i><\/a>, Stochastic Processes and Their Applications, 124 (2014), 3277-3311.<\/li>\n<li>S. Peng, Y. Song and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/33.pdf\" target=\"_blank\" rel=\"noopener\"><i>A Complete Representation Theorem for G-martingales<\/i><\/a>, Stochastics, 86 (2014), 609-631.<\/li>\n<li>T. Pham and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/32.pdf\" target=\"_blank\" rel=\"noopener\"><i>Two Person Zero-sum Game in Weak Formulation and Path Dependent Bellman-Isaacs Equation<\/i><\/a>, SIAM Journal on Control and Optimization, 52 (2014), 2090-2121. <a href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/10\/Game-Correction.pdf\">(An Erratum)<\/a><\/li>\n<li>J. Zhang and J. Zhuo, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/31.pdf\" target=\"_blank\" rel=\"noopener\"><i>Monotone Schemes for Fully Nonlinear Parabolic Path Dependent PDEs<\/i><\/a>, Journal of Financial Engineering, 1 (2014) 1450005 (23 pages); DOI: 10.1142\/S2345768614500056.<\/li>\n<li>I. Ekren, C. Keller, N. Touzi and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/30.pdf\" target=\"_blank\" rel=\"noopener\"><i>On Viscosity Solutions of Path Dependent PDEs<\/i><\/a>, Annals of Probability, 42 (2014), 204-236.<\/li>\n<li>T. Pham and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/29.pdf\" target=\"_blank\" rel=\"noopener\"><i>Some Norm Estimates for Semimartingales<\/i><\/a>, Electronic Journal of Probability, 18 (2013), no. 109, 1-25. <a href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/10\/semimg-correction.pdf\">(An Erratum)<\/a><\/li>\n<li>J. Ma, Q. Song, J. Xu, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/28.pdf\" target=\"_blank\" rel=\"noopener\"><i>Optimal Portfolio Selection under Concave Price Impact<\/i><\/a>, Applied Mathematics and Optimization, 67 (2013), 353-390.<\/li>\n<li>M. Soner, N. Touzi and J. Zhang , <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/27.pdf\" target=\"_blank\" rel=\"noopener\"><i>Dual formulation of the second order target problems<\/i><\/a>, Annals of Applied Probability, 23 (2013), 308-347.<\/li>\n<li>J. Ma, H. Yin and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/26.pdf\" target=\"_blank\" rel=\"noopener\"><i>On Non-Markovian Forward Backward SDEs and Backward Stochastic PDEs<\/i><\/a>, Stochastic Processes and Their Applications, 122 (2012), no. 12, 3980-4004.<\/li>\n<li>J. Cvitanic, J. Ma and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/25.pdf\" target=\"_blank\" rel=\"noopener\"><i>Law of Large Numbers for Self-Exciting Correlated Defaults<\/i><\/a>, Stochastic Processes and Their Applications, 122 (2012), 2781 &#8211; 2810.<\/li>\n<li>M. Soner, N. Touzi and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/24.pdf\" target=\"_blank\" rel=\"noopener\"><i>Wellposedness of Second Order Backward SDEs<\/i><\/a>, Probability Theory and Related Fields, 153 (2012), 149-190.<\/li>\n<li>J. Ma and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/23.pdf\" target=\"_blank\" rel=\"noopener\"><i>On weak solutions of FBSDEs<\/i><\/a>, Probability Theory and Related Fields, 151 (2011), 475-507.<\/li>\n<li>M. Soner, N. Touzi and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/22.pdf\" target=\"_blank\" rel=\"noopener\"><i>Quasi-sure Stochastic Analysis through Aggregation<\/i><\/a>, Electronic Journal of Probability, 16 (2011), 1844-1879.<\/li>\n<li>M. Soner, N. Touzi and J. Zhang,<i>\u00a0M<a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/21.pdf\" target=\"_blank\" rel=\"noopener\">artingale representation theorem for the G-expectation<\/a><\/i>, Stochastic Processes and Their Applications, 121 (2) (2011), 265-287.<\/li>\n<li>I. Kharroubi, J. Ma, H. Pham, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/20.pdf\" target=\"_blank\" rel=\"noopener\"><i>Backward SDEs with constrained jumps and Quasi-Variational Inequalities<\/i><\/a>, Annals of Probability, 38 (2), (2010), 794-840.<\/li>\n<li>S. Hamadene and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/19.pdf\" target=\"_blank\" rel=\"noopener\"><i>The continuous time nonzero-sum Dynkin game problem and application in game options<\/i><\/a>, SIAM Journal on Control and Optimization, 48 (5), (2010), 3659-3669.<\/li>\n<li>S. Hamadene and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/18.pdf\" target=\"_blank\" rel=\"noopener\">Switching problem and related system of reflected BSDEs<\/a>,<\/i> Stochastic Processes and Their Applications, 120 (4), (2010), 403-426.<\/li>\n<li>J. Cvitanic, X. Wan and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/17.pdf\" target=\"_blank\" rel=\"noopener\">Continuous-Time Principal-Agent Problems with Hidden Action and Lump-Sum Payment<\/a>,<\/i> Applied Mathematics and Optimization, 59 (1) (2009), 99-146.<\/li>\n<li>J. Ma, J. Zhang and Z. Zheng, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/16.pdf\" target=\"_blank\" rel=\"noopener\">Weak Solutions for Forward-Backward SDEs&#8212; A Martingale Problem Approach<\/a>,<\/i> Annals of Probability, 36 (6) (2008), 2092-2125.<\/li>\n<li>J. Cvitanic, X. Wan, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/15.pdf\"><i>Principal agent problems with exit options<\/i><\/a>, B.E. Journal of Theoretical Economics, 8 (1) (Contributions) (2008), Article 23.<\/li>\n<li>C. Bender and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/14.pdf\" target=\"_blank\" rel=\"noopener\">Time Discretization and Markovian Iteration for Coupled FBSDEs<\/a>,<\/i> Annals of Applied Probability, 18 (1) (2008), 143-177.<\/li>\n<li>J. Cvitanic and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/13.pdf\" target=\"_blank\" rel=\"noopener\">Optimal Compensation with Adverse Selection and Dynamic Actions<\/a>,<\/i> Mathematics and Financial Economics, 1 (1) (2007), 21-55.<\/li>\n<li>J. Cvitanic, X. Wan and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/12.pdf\" target=\"_blank\" rel=\"noopener\">Optimal contracts in continuous-time models<\/a>,<\/i> Journal of Applied Mathematics and Stochastic Analysis, Volume 2006 (2006), Article ID 95203.<\/li>\n<li>J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/11.pdf\" target=\"_blank\" rel=\"noopener\"><i>Rate of Convergence of Finite Difference Approximations for Degenerate ODEs,<\/i><\/a> Mathematics of Computation, 75 (256) (2006), 1755-1778.<\/li>\n<li>J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/10.pdf\" target=\"_blank\" rel=\"noopener\">The Wellposedness of FBSDEs (II)<\/a>,<\/i> unpublished note.<\/li>\n<li>J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/9.pdf\" target=\"_blank\" rel=\"noopener\">The Wellposedness of FBSDEs<\/a>,<\/i> Discrete and Continuous Dynamical Systems-Series B, 6 (2006), 927-940.<\/li>\n<li>J. Cvitanic and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/8.pdf\" target=\"_blank\" rel=\"noopener\">The Steepest Descent Method for FBSDEs<\/a>,<\/i> Electronic Journal of Probability, 10 (2005), 1468-1495.<\/li>\n<li>J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/7.pdf\" target=\"_blank\" rel=\"noopener\">Representation of Solutions to BSDEs Associated with a Degenerate FSDE<\/a>,<\/i> Annals of Applied Probability, 15 (2005), 1798-1831.<\/li>\n<li>J. Ma and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/6.pdf\" target=\"_blank\" rel=\"noopener\">Representations and regularities for solutions to backward stochastic differential equations with reflections<\/a>,<\/i> Stochastic Processes and Their Applications, 115 (2005), 539-569.<\/li>\n<li>J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/5.pdf\" target=\"_blank\" rel=\"noopener\">A numerical scheme for backward stochastic differential equations<\/a>, <\/i>Annals of Applied Probability, 14 (2004), 459-488.<\/li>\n<li>J. Cvitanic, J. Ma, and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/4.pdf\" target=\"_blank\" rel=\"noopener\">Efficient computation of delta-hedges for options with discontinuous payoffs<\/a>,<\/i> Mathematical Finance, 13 (2003), 135-151.<\/li>\n<li>J. Ma and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/3.pdf\" target=\"_blank\" rel=\"noopener\">Representation theorems for backward stochastic differential equations<\/a>,<\/i> Annals of Applied Probability, 12 (2002), 1390-1418.<\/li>\n<li>J. Ma and J. Zhang, <i><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/2.pdf\" target=\"_blank\" rel=\"noopener\">Path regularity of solutions to backward stochastic differential equations<\/a>,<\/i> Probability Theory and Related Fields, 122 (2002), 163-190.<\/li>\n<li>J. Ma, P. Protter, and J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/1.pdf\" target=\"_blank\" rel=\"noopener\"><i>Explicit form and path regularity of martingale representations<\/i><\/a>, Levy Processes &#8211; Theory and Applications, O.E.Barndorff-Nielsen, T. Mikosch and S.I. Resnick (Eds.), Birkhauser Boston,(2001), 337-360.<\/li>\n<\/ul>\n<p><!--more--><\/p>\n<p><!--more--><\/p>\n<h2>PhD Thesis<\/h2>\n<ul>\n<li>J. Zhang, <a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/thesis.pdf\" target=\"_blank\" rel=\"noopener\"><i>Some fine properties of backward stochastic differential equations, with applications<\/i><\/a>, Ph.D. dissertation, Purdue University, (2001).<\/li>\n<\/ul>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":370,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-content-detail.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-353","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Publications - Jianfeng Zhang<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/publications\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Publications - 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