{"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":"2026-04-12T21:59:34","modified_gmt":"2026-04-13T04:59:34","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  <h3>Books<\/h3>\n<ul>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/book1.pdf\">J. Cvitanic and J. Zhang<\/a>, <i>Contract theory in continuous-time models<\/i>, 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><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/book2.pdf\">J. Zhang<\/a>, <i>Backward Stochastic Differential Equations &#8212; from linear to fully nonlinear theory<\/i>, 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<h3>Papers<\/h3>\n<ul>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/03\/GZ-information.pdf\">Z. Gu and J. Zhang<\/a>, \u00a0<i><i>On Information Controls<\/i><\/i><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2602.07318.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/12\/MXZ-insider.pdf\">J. Ma, W. Xia and J. Zhang<\/a>, \u00a0<i><i>Wealth or Stealth? The Camouflage Effect in Insider Trading<\/i><\/i><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2512.06309.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/10\/MXZ-nonconvex.pdf\">J. Ma, W. Xia and J. Zhang<\/a>, \u00a0<i>Characterizing Nonconvex Boundaries via Scalarization<\/i><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2510.09918.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/06\/QZ-Insider.pdf\">B. Qiao and J. Zhang<\/a>,\u00a0<i>A New Approach for the Continuous Time <i>Kyle-Back Strategic Insider Equilibrium Problem<\/i><\/i><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2506.12281.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/03\/MZZ-Volatility.pdf\">C. Mou, J. Zhang and J. Zhou<\/a>, <em><em>Second-order monotonicity conditions and mean field games with volatility control<\/em><\/em><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2503.10097.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2024\/11\/STZ-Occupied.pdf\">M. Soner, V. Tissot-Daguette, and J. Zhang<\/a>, <em>Controlled Occupied Processes and Viscosity Solutions<\/em><i><i>,<\/i><\/i><em><em>\u00a0<\/em><\/em>preprint, arXiv:2411.12080.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/Efficiency.pdf\">J. Zhang<\/a>, <em><em><em>Instability and Efficiency of Non-cooperative Games<\/em><\/em><\/em><em><em>, <\/em><\/em>preprint, arXiv:2405.17196.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/TZZ.pdf\">J. Zhou, N. Touzi, and J. Zhang<\/a>, <em><em><em>Viscosity Solutions for HJB Equations on the Process Space: Application to Mean Field Control with Common Noise<\/em><\/em><\/em><em><em>, <\/em><\/em>preprint, arXiv:2401.04920.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/LZ-voting.pdf\">A. Lazrak and J. Zhang<\/a>, <i>Unlocking Democratic Efficiency: How Coordinated <i>Outcome-Contingent Promises Shape Decisions<\/i><\/i>, preprint, arXiv:2304.08008.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/08\/IZ-SVHJB.pdf\">M. Iseri and J. Zhang<\/a>, <em><em>Set Valued Hamilton-Jacobi-Bellman Equations, <\/em><\/em>Annals of Probability, accepted, arXiv:2311.05727.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/04\/MWZ-PIA.pdf\">J. Ma, G. Wang, and J. Zhang<\/a>, <i>Convergence Analysis<\/i><i> for Entropy-Regularized <i>Control Problems: a Probabilistic Approach<\/i><\/i><em><em>, <\/em><\/em>SIAM Journal on Control and Optimization, 64 (2026), 816-842.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2026\/01\/QZ-Hamiltonian.pdf\">B. Qiao and J. Zhang<\/a>,\u00a0<i>Set Values of Dynamic Nonzero Sum Games and <i>Set Valued Hamiltonians,<\/i><\/i> SIAM Journal on Control and Optimization, 64 (2026), 316-334.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/11\/ZZ-PA.pdf\">J. Zhang and Z. Zhu<\/a>, <em>A Dynamic Principal Agent Problem with One-sided Commitment<\/em>, Mathematics of Operations Research, 50 (2025), 2600-2632.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/09\/MZ-anti.pdf\">C. Mou and J. Zhang<\/a>, <em>Mean Field Game Master Equations with Anti-monotonicity Conditions<\/em>, Journal of the European Mathematical Society, 27 (2025), 4469-4499.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2025\/01\/Iseri-Zhang.pdf\">M. Iseri and J. Zhang<\/a>, <em>Set Values for Mean Field Games<\/em>, Transactions of the AMS, \u00a0377 (2024), 7117-7174.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/MZ-Master.pdf\">C. Mou and J. Zhang<\/a>, <em>Wellposedness of Second Order Master Equations for Mean Field Games with Nonsmooth Data<\/em>, Memoirs of the AMS, 302(2024), no. 1515.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2024\/10\/TTZ3.pdf\">M. Talbi, N. Touzi, and J. Zhang<\/a>, <i>From finite population optimal stopping to mean field optimal stopping<\/i>, Annals of Applied Probability, 34(2024), \u00a04237-4267.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2024\/05\/MZ-EMFG.pdf\">C. Mou and J. Zhang<\/a>, <em>Minimal Solutions of Master Equations for Extended Mean Field Games<\/em>, Journal des Math\u00e9matiques Pures et Appliqu\u00e9es, 184(2024), 190-217.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/11\/InconsistentExample.pdf\">J. Zhang<\/a>, <i>Is a sophisticated agent always a wise one? <\/i>SIAM Journal on Financial Mathematics Short Communications, 14(2023), SC42-SC48.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/11\/FZ-cubature.pdf\">Q. Feng and J. Zhang<\/a>, <em>Cubature Method for Stochastic Volterra Integral Equations<\/em>, SIAM Journal on Financial Mathematics, 14(2023), 959-1003.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/08\/YZ-JinPreface.pdf\">S. Yao and J. Zhang<\/a>, \u00a0<em>Preface: A Tribute to Professor Jin Ma on His 65th Birthday<\/em>, Numerical Algebra, Control and Optimization, 13 (3\\&amp;4), 2023, <i>pp. i-ii, <\/i>doi:10.3934\/naco.202303i.<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/08\/TTZ.pdf\">M. Talbi, N. Touzi, and J. Zhang<\/a>, <em>Dynamic Programming Equation for the Mean Field Optimal Stopping Problem<\/em>, SIAM Journal on Control and Optimization, 61 (2023), <span class=\"\" data-v-3708431c=\"\">\u00a02140-2164.<\/span><\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/08\/TTZ2.pdf\">M. Talbi, N. Touzi, and J. Zhang<\/a>, <em>Viscosity Solutions for Obstacle Problems on Wasserstein Space<\/em>, SIAM Journal on Control and Optimization, 61 (2023), 1712-1736.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/GMMZ.pdf\">W. Gangbo, A. Meszaros, C. Mou, and J. Zhang<\/a>, <em>Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity<\/em>, Annals of Probability, 50 (2022), 2178-2217.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/MZ-MFGC.pdf\">C. Mou and J. Zhang<\/a>, <em>Mean Field Games of Controls: Propagation of Monotonicities<\/em>, Probability, Uncertainty and Quantitative Risk, 7 (2022), 247-274.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/WYZ.pdf\">H. Wang, J. Yong, and J. Zhang<\/a>, <em>Path Dependent Feynman-Kac Formual for Forward Backward Stochastic Volterra Integral Equations<\/em>, Annales de l&#8217;Institut Henri Poincare, 58 (2022), 603-638.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/FRZ.pdf\">Z. Feinstein, B. Rudloff, and J. Zhang<\/a>, <em>Dynamic Set Values for Nonzero Sum Games with Multiple Equilibriums<\/em>, Mathematics of Operations Research, 47 (2022), 616-642.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/MWZ.pdf\">J. Ma, T.K. L. Wong and J. Zhang<\/a>, <em>Time-consistent Conditional Expectation under Probability Distortion<\/em>, Mathematics of Operations Research, 46 (2021), 1149-1180.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/YZ-example.pdf\">J. Yong and J. Zhang<\/a>, <em>Non-Equivalence of Stochastic Optimal Control Problems with Open and Closed Loop Controls<\/em>, Systems and Control Letters, 153 (2021), 104948.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/BKMZ.pdf\">R. Buckdahn, C. Keller, J. Ma and J. Zhang<\/a>, <i>Fully Nonlinear Stochastic and Rough PDEs: Classical and Viscosity Solutions<\/i>, Probability, Uncertainty and Quantitative Risk, (2020) 5:7, DOI: 10.1186\/s41546-020-00049-8.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/PTZ.pdf\">D. Possamai, N. Touzi and J. Zhang<\/a>, <i><em>Zero-sum Path-dependent Stochastic Differential Games in Weak Formulation<\/em><\/i>, Annals of Applied Probability, 30 (2020), 1415-1457.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/WZ-derivative.pdf\">C. Wu and J. Zhang<\/a>, <i>An Elementary Proof for the Structure of Wasserstein Derivatives<\/i>, unpublished note.<\/li>\n<li><a href=\"https:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/07\/WZ-master-1.pdf\">C. Wu and J. Zhang<\/a>, <i>Viscosity Solutions to Parabolic Master Equations and McKean-Vlasov SDEs with Closed-loop Controls<\/i>, Annals of Applied Probability, 30 (2020), 936-986.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/RTZ-semilinear.pdf\">Z. Ren, N. Touzi and J. Zhang <\/a>, <i>Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs<\/i>, SIAM Journal on Control and Optimization, 58 (2020), 277-302.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/VZ-fBM.pdf\">F. Viens and J. Zhang<\/a>, <i>A Martingale Approach for Fractional Brownian Motions and Related Path Dependent PDEs <\/i>, Annals of Applied Probability, 29 (2019), 3489-3540.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/SZ.pdf\">Y. Saporito and J. Zhang<\/a>, <i>Stochastic Control with Delayed Information and Related Nonlinear Master Equation <\/i>, SIAM Journal on Control and Optimization, 57 (2019), 693-717.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/WZ-FBSDE.pdf\">H. Wang and J. Zhang<\/a>, <i>Forward Backward SDEs in Weak Formulation<\/i>, Mathemtical Control and Related Fields, 8 (2018), 1021-1049.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/48.pdf\">C. Karnam, J. Ma and J. Zhang <\/a>, <i>Dynamic Approaches for Some Time Inconsistent Optimization Problems<\/i>, Annals of Applied Probability, 27 (2017), 3435-3477.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/47.pdf\">Z. Ren, N. Touzi and J. Zhang <\/a>, <i>Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs<\/i>, SIAM Journal on Mathematical Analysis, 49 (2017), 4093-4116.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/46.pdf\">J. Diehl and J. Zhang <\/a>, <i>Backward Stochastic Differential Equations with Young Drift<\/i>, Probability, Uncertainty and Quantitative Risk, (2017) 2:5 DOI 10.1186\/s41546-017.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/45.pdf\">I. Ekren and J. Zhang <\/a>, <i>Pseudo-Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs<\/i>, Probability, Uncertainty and Quantitative Risk, (2016) 1:6, DOI 10.1186\/s41546-016-0010-3.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/44.pdf\">J. Ma, Z. Ren, N. Touzi and J. Zhang <\/a>, <i>Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation <\/i>, 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><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/43.pdf\">I.Ekren, N. Touzi and J. Zhang <\/a>, <i>Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part II<\/i>, Annals of Probability, 44 (2016), 2507-2553.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/42.pdf\">I. Ekren, N. Touzi and J. Zhang <\/a>, <i>Viscosity Solutions of Fully Nonlinear Parabolic Path Dependent PDEs: Part I<\/i>, Annals of Probability, 44 (2016), 1212-1253.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/41.pdf\">C. Keller and J. Zhang <\/a>, <i>Pathwise Ito Calculus for Rough Paths and Rough PDEs with Path Dependent Coefficients<\/i>, Stochastic Processes and Their Applications, 126 (2016), 735-766.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/40.pdf\">J. Ma, X. Wang and J. Zhang<\/a>, <i>Dynamic Equilibrium Limit Order Book Model and Optimal Execution Problem <\/i>, Mathematical Control and Related Fields, 5 (2015), 557-583.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/39.pdf\">M. Nutz and J. Zhang<\/a>, <i>Optimal Stopping under Adverse Nonlinear Expectation and Related Games <\/i>, Annals of Applied Probability, 25 (2015), 2503-2534.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/38.pdf\">J. Ma, Z. Wu, D. Zhang and J. Zhang<\/a>, <i>On Wellposedness of Forward-Backward SDEs &#8212; A Unified Approach<\/i>, Annals of Applied Probability, 25 (2015), 2168-2214.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/37.pdf\">R. Buckdahn, J. Ma and J. Zhang<\/a>, <i>Pathwise Taylor Expansions for Random Fields on Multiple Dimensional Paths <\/i>, Stochastic Processes and Their Applications, 125 (2015), 2820-2855.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/36.pdf\">W. Guo, J. Zhang and J. Zhuo<\/a>, <i>A Monotone Scheme for High Dimensional Fully Nonlinear PDEs<\/i>, Annals of Applied Probability, 25 (2015), 1540-1580.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/35.pdf\">Z. Ren, N. Touzi and J. Zhang <\/a>, <i>An Overview of Viscosity Solutions of Path Dependent PDEs<\/i>, Stochastic Analysis and Applications, 2014, 100 (2014), 397-453.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/34.pdf\">I. Ekren, N. Touzi and J. Zhang <\/a>, <i>Optimal Stopping under Nonlinear Expectation<\/i>, Stochastic Processes and Their Applications, 124 (2014), 3277-3311.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/33.pdf\">S. Peng, Y. Song and J. Zhang<\/a>, <i>A Complete Representation Theorem for G-martingales<\/i>, Stochastics, 86 (2014), 609-631.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/32.pdf\">T. Pham and J. Zhang<\/a>, <i>Two Person Zero-sum Game in Weak Formulation and Path Dependent Bellman-Isaacs Equation<\/i>, 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><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/31.pdf\">J. Zhang and J. Zhuo<\/a>, <i>Monotone Schemes for Fully Nonlinear Parabolic Path Dependent PDEs <\/i>, Journal of Financial Engineering, 1 (2014) 1450005 (23 pages); DOI: 10.1142\/S2345768614500056.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/30.pdf\">I. Ekren, C. Keller, N. Touzi and J. Zhang <\/a>, <i>On Viscosity Solutions of Path Dependent PDEs<\/i>, Annals of Probability, 42 (2014), 204-236.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/29.pdf\">T. Pham and J. Zhang<\/a>, <i>Some Norm Estimates for Semimartingales<\/i>, 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><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/28.pdf\">J. Ma, Q. Song, J. Xu, and J. Zhang<\/a>, <i>Optimal Portfolio Selection under Concave Price Impact<\/i>, Applied Mathematics and Optimization, 67 (2013), 353-390.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/27.pdf\">M. Soner, N. Touzi and J. Zhang <\/a>, <i>Dual formulation of the second order target problems<\/i>, Annals of Applied Probability, 23 (2013), 308-347.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/26.pdf\">J. Ma, H. Yin and J. Zhang<\/a>, <i>On Non-Markovian Forward Backward SDEs and Backward Stochastic PDEs<\/i>, Stochastic Processes and Their Applications, 122 (2012), no. 12, 3980-4004.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/25.pdf\">J. Cvitanic, J. Ma and J. Zhang <\/a>, <i>Law of Large Numbers for Self-Exciting Correlated Defaults<\/i>, Stochastic Processes and Their Applications, 122 (2012), 2781 &#8211; 2810.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/24.pdf\">M. Soner, N. Touzi and J. Zhang<\/a>, <i>Wellposedness of Second Order Backward SDEs<\/i>, Probability Theory and Related Fields, 153 (2012), 149-190.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/23.pdf\">J. Ma and J. Zhang<\/a>, <i>On weak solutions of FBSDEs<\/i>, Probability Theory and Related Fields, 151 (2011), 475-507.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/22.pdf\">M. Soner, N. Touzi and J. Zhang<\/a>, <i>Quasi-sure Stochastic Analysis through Aggregation<\/i>, Electronic Journal of Probability, 16 (2011), 1844-1879.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/21.pdf\">M. Soner, N. Touzi and J. Zhang, <\/a>, <i>Martingale representation theorem for the G-expectation<\/i>, Stochastic Processes and Their Applications, 121 (2) (2011), 265-287.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/20.pdf\">I. Kharroubi, J. Ma, H. Pham, and J. Zhang<\/a>, <i>Backward SDEs with constrained jumps and Quasi-Variational Inequalities<\/i>, Annals of Probability, 38 (2), (2010), 794-840.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/19.pdf\">S. Hamadene and J. Zhang<\/a>, <i>The continuous time nonzero-sum Dynkin game problem and application in game options<\/i>, SIAM Journal on Control and Optimization, 48 (5), (2010), 3659-3669.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/18.pdf\">S. Hamadene and J. Zhang<\/a>, <i>Switching problem and related system of reflected BSDEs,<\/i> Stochastic Processes and Their Applications, 120 (4), (2010), 403-426.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/17.pdf\">J. Cvitanic, X. Wan and J. Zhang<\/a>, <i>Continuous-Time Principal-Agent Problems with Hidden Action and Lump-Sum Payment,<\/i> Applied Mathematics and Optimization, 59 (1) (2009), 99-146.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/16.pdf\">J. Ma, J. Zhang and Z. Zheng<\/a>, <i>Weak Solutions for Forward-Backward SDEs&#8212; A Martingale Problem Approach,<\/i> Annals of Probability, 36 (6) (2008), 2092-2125.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/15.pdf\">J. Cvitanic, X. Wan, and J. Zhang<\/a>, <i>Principal agent problems with exit options<\/i>, B.E. Journal of Theoretical Economics, 8 (1) (Contributions) (2008), Article 23.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/14.pdf\">C. Bender and J. Zhang<\/a>, <i>Time Discretization and Markovian Iteration for Coupled FBSDEs,<\/i> Annals of Applied Probability, 18 (1) (2008), 143-177.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/13.pdf\">J. Cvitanic and J. Zhang<\/a>, <i>Optimal Compensation with Adverse Selection and Dynamic Actions,<\/i> Mathematics and Financial Economics, 1 (1) (2007), 21-55.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/12.pdf\">J. Cvitanic, X. Wan and J. Zhang<\/a>, <i>Optimal contracts in continuous-time models,<\/i> Journal of Applied Mathematics and Stochastic Analysis, Volume 2006 (2006), Article ID 95203.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/11.pdf\">J. Zhang<\/a>, <i>Rate of Convergence of Finite Difference Approximations for Degenerate ODEs,<\/i> Mathematics of Computation, 75 (256) (2006), 1755-1778.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/10.pdf\">J. Zhang<\/a>, <i>The Wellposedness of FBSDEs (II),<\/i> unpublished note.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/9.pdf\">J. Zhang<\/a>, <i>The Wellposedness of FBSDEs,<\/i> Discrete and Continuous Dynamical Systems-Series B, 6 (2006), 927-940.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/8.pdf\">J. Cvitanic and J. Zhang<\/a>, <i>The Steepest Descent Method for FBSDEs,<\/i> Electronic Journal of Probability, 10 (2005), 1468-1495.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/7.pdf\">J. Zhang<\/a>, <i>Representation of Solutions to BSDEs Associated with a Degenerate FSDE,<\/i> Annals of Applied Probability, 15 (2005), 1798-1831.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/6.pdf\">J. Ma and J. Zhang<\/a>, <i>Representations and regularities for solutions to backward stochastic differential equations with reflections,<\/i> Stochastic Processes and Their Applications, 115 (2005), 539-569.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/5.pdf\">J. Zhang<\/a>, <i>A numerical scheme for backward stochastic differential equations, <\/i>Annals of Applied Probability, 14 (2004), 459-488.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/4.pdf\">J. Cvitanic, J. Ma, and J. Zhang<\/a>, <i>Efficient computation of delta-hedges for options with discontinuous payoffs,<\/i> Mathematical Finance, 13 (2003), 135-151.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/3.pdf\">J. Ma and J. Zhang<\/a>, <i>Representation theorems for backward stochastic differential equations,<\/i> Annals of Applied Probability, 12 (2002), 1390-1418.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/2.pdf\">J. Ma and J. Zhang<\/a>, <i>Path regularity of solutions to backward stochastic differential equations,<\/i> Probability Theory and Related Fields, 122 (2002), 163-190.<\/li>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/1.pdf\">J. Ma, P. Protter, and J. Zhang<\/a>, <i>Explicit form and path regularity of martingale representations<\/i>, 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<h3>PhD Thesis<\/h3>\n<ul>\n<li><a href=\"http:\/\/dornsife.usc.edu\/jianfeng-zhang\/wp-content\/uploads\/sites\/240\/2023\/06\/thesis.pdf\">J. Zhang<\/a>, <i>Some fine properties of backward stochastic differential equations, with applications<\/i>, 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 v27.1.1 - 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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