Book

Ma, Jin and Yong, Jiongmin (1999)

Forward-Backward Stochastic Differential Equations and their Applications

Lecture Notes in Mathematics (1702), Springer-Verlag, Berlin

Submitted Papers

  • Ma, J. and Tan, Y. (2023), A Generalized Kyle-Back Strategic Insider Trading Model with Dynamic Information, submitted [pdf]

Papers in Press

  • Ararat, C., Ma, J., Wu, W. (2023), Set-Valued Backward Stochastic Differential Equations. Annals of Applied Probability, to appear. [pdf]
  • Buckdahn, R., Li, J., Ma, J. (2023), A General Conditional McKean-Vlasov Stochastic Differential Equation. Annals of Applied Probability, to appear. [pdf]

Selected Papers in Journals

  • Ma, J. and Noh, E. (2022), Equilibrium model of limit order books: a mean-field game view. Stochastic analysis, filtering, and stochastic optimization, 381–410, Springer, Cham, [2022], ©2022. [pdf]
  • Bai, L. and Ma, J. (2021), Optimal investment and dividend strategy under renewal risk model. SIAM J. Control Optim. 59, no. 6, 4590–4614. [pdf]
  • Ma, J., Wong, T. L., Zhang, J. (2021), Time-Consistent Conditional Expectation under Probability Distortion. Mathematics of Operations Research. Vol. 12 (15), pp. 1-32. [pdf]
  • Buckdahn, R., Keller, C., Ma, J., Zhang, J. (2020), Fully Nonlinear Stochastic and Rough PDEs: Classical and Viscosity Solutions. Probability, Uncertainty, and Quantative Risk. Vol. 5 (7), pp. 1-59. [pdf]
  • Ma, J., Sun, R., and Zhou, Y. (2018), Kyle-Back Equilibrium Models and Linear Conditional Mean-field SDEs. SIAM J. Control Optim. 56, no. 2, 1154-1180. [pdf]
  • Chen, J., Ma, J., Yin, H. (2018), Forward-backward SDEs with Dicontinuous Coefficients. Stoch. Anal. Appl. 36, no. 2, 274-294. [pdf]
  • Bai, L., Ma, J., Xing, X. (2017), Optimal Dividend and Investment Problems under Sparrer-Andersen Model. Annals of Applied Probability, 27, no.6, 3588-3632. [pdf]
  • Karnam, C., Ma, J., Zhang, J. (2017), Dynamic Approaches for Some Time Inconsistent Optimization Problems. Annals of Applied Probability, 27, no.6, 3435-3477. [pdf]
  • Buckdahn, R., Li, J., and Ma, J. (2017), A Mean-field Stochastic Control Problem with Partial Observations. Annals of Applied Probability, 27, no.5, 3201-3245. [pdf]
  • Buckdahn, R., Li, J., Ma, J. (2016). A Stochastic Maximum Principle for General Mean-field Systems. Applied Mathematics and Optimization. 74, no.3, 507-534.  [pdf]
  • Ma, J., Ren, Z., Touzi, N., Zhang, J. (2016). Large Deviation for Non-Markovian Diffusions and a Path-dependent Eikonal Equation. Annales de l’institut Henri Poincare, Probab. Stat. Vol. 52 (no. 3), pp. 1196-1216. [pdf]
  • Buckdahn, R., Ma, J., Zhang, J. (2015). Pathwise Taylor Expansions for Random Fields on Multi-dimensional Paths. Stochastic Process. Appl. 125, no. 7, 2820–2855. [pdf]
  • Ma, J., Wang, X., Zhang, J. (2015). Dynamic Equilibrium Models for Limit Order Book and Optimal Execution Problems. Math. Control Relat. Fields 5, no. 3, 557–583. [pdf]
  • Ma, J., Wu, Z., Zhang, D., Zhang, J. (2015). On Wellposedness of Forward-Backward SDEs — A Unified Approach. Ann. Appl. Probab. 25, no. 4, 2168–2214. [pdf]
  • Bai, L., Ma, J. (2015). Stochastic differential equations driven by fractional Brownian motion and Poisson point process. Bernoulli 21, no. 1, 303–334. [pdf]
  • Ma, J., Song, Q., Xu, J., Zhang, J. (2013). Optimal Portfolio Selection Under Concave Price Impact. Appl. Math. Optim. 67, no. 3, 353–390. [pdf]
  • Ma, J., Yin, H., Zhang, J. (2012). On Non-Markovian Forward Backward SDEs and Backward Stochastic PDEs. Stochastic Process. Appl. 122, no. 12, 3980–4004. [pdf]
  • Cvitanic, J., Ma, J., Zhang, J. (2012). Law of Large Numbers for Self-Exciting Correlated Defaults. Stochastic Process. Appl. 122, no. 8, 2781–2810. [pdf]
  • Buchdahn, R., Bulla, I., Ma, J. (2011). Pathwise Taylor Expansions for Ito Type Random Fields. Math. Control Relat. Fields 1, no. 4, 437–468. [pdf]
  • Ma, J., Zhang, J. (2011). On Weak Solutions of Forward-Backward Stochastic Differential Equations. Probab. Theory Related Fields 151, no. 3-4, 475–507. [pdf]
  • Figueroa-Lopez, E., Ma, J. (2010). Optimal portfolios in Lévy markets under state-dependent bounded utility functions. Int. J. Stoch. Anal., Art. ID 236587, 27 pp. [pdf]
  • Ma, J., Yao, S. (2010). Quadratic g-Expectations and the Associated Doob-Meyer Decompostion. Stoch. Anal. Appl. 28, no. 4, 711–734. [pdf]
  • Kharroubi, I., Ma, J., Pham, H., Zhang, J. (2010). Backward SDEs with constrained jumps and quasi-variational inequalities. Ann. Probab. 38, no. 2, 794–840. [pdf]
  • Ma, J., Yong, J., Zhao, Y. (2010). General Forward-Backward Stochastic Differential Equations of Markovian Type. J. Syst. Sci. Complex. 23, no. 3, 546–571. [pdf]
  • Ma, J., Yun, Y. (2010). Correlated intensity, counter party risks, and dependent mortalities. Insurance Math. Econom. 47, no. 3, 337–351. [pdf]
  • Jien, Y. and Ma, J. (2009). Stochastic Differential Equations Driven by Fractional Brownian Motions. Bernoulli. Vol. 15 (3), pp. 846-870.
  • Liu, Y., Ma, J. (2009). Optimal Reinsurance/Investment for General Insurance Models. The Annals of Applied Probability. Vol. 19 (4), pp. 1495–1528. [pdf]
  • Ma, J. and Wang, Y. (2009). On Variant Reflected Backward SDEs and Applications. J. Appl. Math. Stoch. Anal. Vol. Art. ID 854768, pp. 26. [pdf]
  • Ma, J., Zhang, J., Zheng, Z. (2008). Weak Solutions for Backward Stochastic Differential Equations, A Martingale Approach. The Annals of Probability. Vol. 36 (6), pp. 2092–2125. [pdf]
  • Ma, J., Shen, J., Zhao, Y. (2008). Numerical Method for Forward-Backward Stochastic Differential Equations. SIAM Journal on Numerical Analysis. Vol. 46 (5), pp. 2636–2661. [pdf]
  • Hu, Y., Ma, J., Peng, S., Yao, S. (2008). Representation Theorems for Quadratic F-Consistent Nonlinear Expectations. Stochastic Processes and Their Applications. Vol. 118 (9), pp. 1518-1551. [pdf]
  • Buckdahn, R. and Ma, J., Rainer, C. (2008),  Stochastic Control Problems for Systems Driven by Normal Martingales. The Annals of Applied Probability. Vol. 18 (2), pp. 632–663. [pdf]
  • Buckdahn, R. and Ma, J. (2007),  Pathwise Stochastic Control Problems and Stochastic HJB Equations,  SIAM Journal on Control and Optimizations, Vol. 45, no.6; 2224-2256. [pdf]
  • Ma, J. and Yuhua Y., (2006), Principle of Equivalent Utility and Universal Variable Life Insurance, Scandinavian Actuarial Journal. Vol. 2006 (6), pp. 311–337. [pdf]
  • Ma, J., and Zhang, J. (2005),  Representation and Path Regularities for Solution to BSDE’s with Reflections,  Stochastic Processes and their Applications, Vol. 115, no. 4; 539 – 569. [pdf]
  •  Hu, Y., and Ma, J. (2004),  Nonlinear Feynman-Kac Formula and Discrete Functional-type BSDEs with Continuous Coefficients,  Stochastic Processes and their Applications, Vol. 112,  no.1; 23-51.  [pdf]
  •  Galea, M., Ma, J., and Torres, S. (2003),  Price Calculation for Jump-Diffusion Models Involving Power Exponential Distributions. Stochastic models (Mexico City, 2002), 137–160, Contemp. Math., 336, Amer. Math. Soc., Providence, RI, 2003.   [pdf]
  •  Ma, J., and Sun, X. (2003),  Ruin Probability for Insurance Models Involving Investments.  Scandinavian Actuarial Journal,  No. 3; 217-237.   [pdf]
  • Antonelli, F., and Ma, J. (2003),  Weak Solutions of Forward-Backward SDE’s.  Stochastic  Analysis and Applications,  Vol. 21, No. 3;  493-514.   [pdf]
  • Buckdahn, R., and Ma, J. (2002),  Pathwise Stochastic Taylor Expansions and Stochastic Viscosity Solutions for Fully Nonlinear Stochastic PDEs. Annals of Probability, Vol. 30, No. 3; 1131-1171.    [pdf]
  • Cvitanic, J., Ma., J, and Zhang, J. (2002),  Efficient Computation of Hedging Portfolios for Options with Discontinuous Payoffs.  Mathematical Finance, Vol. 13,  No.1; 131-151.   [pdf]
  • Hu, Y., Ma, J., and Yong, J. (2002),  On Semi-linear Degenerate Backward Stochastic Partial Differential Equations.  Probability Theory and Related Fields, 123, No. 3; 381-411.  [pdf]
  • Ma, J., and Zhang, J. (2002),  Representation Theorems for Backward StochasticDifferential Equations. Annals of Applied Probability,  Vol. 12 No. 4; 1390-1418.    [pdf]
  • Ma, J., and Zhang, J. (2002),  Path Regularity for Solutions of Backward SDE’s. Probability Theory and Related Fields, 122; 163-190. [pdf]
  • Ma, J., and Yong, J. (2002),  Approximate Solvability of Forward-Backward Stochastic Differential Equations.  Applied Mathematics & Optimization, 45; 1-22.   [pdf]
  • Ma, J., Protter, P., San Martin, J., and Torres, S. (2002),  Numerical Method for Backward SDE’s.  Annals of Applied Probability, 12 (1); 302-316.   [pdf]
  • Buckdahn, R., and Ma, J. (2001),  Stochastic Viscosity Solutions for Nonlinear Stochastic Partial Differential Equations, Part II.  Stochastic Processes and their Applications, 93; 205-228.  [pdf]
  • Buckdahn, R., and Ma, J. (2001),  Stochastic Viscosity Solutions for Nonlinear Stochastic Partial Differential Equations, Part I.  Stochastic Processes and their Applications, 93; 181-204.    [pdf]
  • Cvitanic, J., and Ma, J. (2001),  Reflected Forward-Backward SDE’s and Obstacle Problems with Boundary Conditions.  Journal of Applied Mathematics and Stochastic Analysis, 14 (2); 113-138. [pdf]
  • Ma, J., Protter, P., and Zhang, J. (2001),  Explicit Form and Path Regularity of Martingale Representations.  Lévy Processes, Theory and Applications, O. Barndorff-Nielsen, T. Mikosch, S. Resnick, eds., Birkhauser, 339-362. [pdf]
  • Ma, J., and Yong, J. (1999),  Dynamic Programming for Multidimensional Stochastic Control Problems.  Acta Mathematica Sinica, 15(4); 485-506.   [pdf]
  •  Ma, J., and Zajic, T. (1999), Rough Asymptotics of Forward-Backward SDE’s, “Control of Distributed Parameter and Stochastic Systems,” (S. Chen, X. Li, J. Yong, X. Zhou, eds.), Kluwer, Academic Publishers, 239-246.
  • Ma, J., and Yong, J. (1999),  On Linear Degenerate Backward Stochastic PDE’s. Probability Theory and Related Fields, 113; 135-170.   [pdf]
  •  Ma, J., Protter, P., and San Martin, J. (1998),  Anticipating Integrals for a Class of Martingales.  Bernoulli, 4(1); 81-114. [pdf]
  • Ma, J., and Yong, J. (1997),  Adapted Solution of a Degenerate Backward Stochastic PDE,  with Applications.  Stochastic Processes and Their Applications, 70(1);  59-84. [pdf]
  • Douglas, Jr., J., Ma, J., and Protter, P. (1996),  Numerical Method for Forward-Backward Stochastic Differential Equations.  The Annals of Applied Probability,  6(3); 940-968. [pdf]
  • Cvitanic, J., and Ma, J. (1996),  Hedging Options for a Large Investor and Forward-Backward SDEs. The Annals of Applied Probability, 6(2); 370-398. [pdf]
  • Ma, J., and Yong, J. (1995),  Solvability of Forward-Backward SDEs and the Nodal Set of Hamilton-Jacobi-Bellman Equations.  Chinese Annals of Mathematics, 16B(3); 279-298.
  •  Duffie, D., Ma, J., and Yong, J. (1995),  Black’s Consol Rate Conjecture.  The Annals of Applied Probability, 5(2); 356-382.   [pdf]
  • Ma, J., Protter, P., and Yong, J. (1994),  Solving Forward-Backward Stochastic Differential Equations Explicitly-A Four Step Scheme.  Probability Theory and Related Fields, 98; 339-359.   [pdf]
  • Ma, J. (1994),  Singular Stochastic Control for Diffusions and SDE with Discontinuous  Paths and Reflecting Boundary Conditions.  Stochastics and Stochastics Reports, 46; 161-192.   [pdf]
  • Ma, J. (1993),  Discontinuous Reflection and A Class of Singular Stochastic Control Problems for Diffusions.  Stochastics and Stochastics Reports, 44; 225-252.   [pdf]
  • Ma, J. (1992),  On the Principle of Smooth Fit for a Class of Singular Stochastic Control Problems. Society of Industrial and Applied Mathematics Journal on Control and Optimization, 30(4); 975-999.  [pdf]