July  2006, 6(4): 927-940. doi: 10.3934/dcdsb.2006.6.927

The wellposedness of FBSDEs

1. 

USC Mathematics Department, 3620 Vermont Ave, KAP 108, Los Angeles, CA 90089, United States

Received  January 2005 Revised  September 2005 Published  April 2006

In this paper we investigate the wellposedness of a class of Forward-Backward SDEs. Compared to the existing methods in the literature, our result has the following features: (i) arbitrary time duration; (ii) random coefficients; (iii) (possibly) degenerate forward diffusion; and (iv) no monotonicity condition. As a trade off, we impose some assumptions on the derivatives of the coefficients. A comparison theorem is also proved under the same conditions. This work is motivated by studying numerical methods for FBSDEs.
Citation: Jianfeng Zhang. The wellposedness of FBSDEs. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 927-940. doi: 10.3934/dcdsb.2006.6.927
[1]

Kaitong Hu, Zhenjie Ren, Nizar Touzi. On path-dependent multidimensional forward-backward SDEs. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022010

[2]

Haiyang Wang, Jianfeng Zhang. Forward backward SDEs in weak formulation. Mathematical Control and Related Fields, 2018, 8 (3&4) : 1021-1049. doi: 10.3934/mcrf.2018044

[3]

Jiongmin Yong. Forward-backward evolution equations and applications. Mathematical Control and Related Fields, 2016, 6 (4) : 653-704. doi: 10.3934/mcrf.2016019

[4]

Fabio Paronetto. Elliptic approximation of forward-backward parabolic equations. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1017-1036. doi: 10.3934/cpaa.2020047

[5]

G. Bellettini, Giorgio Fusco, Nicola Guglielmi. A concept of solution and numerical experiments for forward-backward diffusion equations. Discrete and Continuous Dynamical Systems, 2006, 16 (4) : 783-842. doi: 10.3934/dcds.2006.16.783

[6]

Xin Chen, Ana Bela Cruzeiro. Stochastic geodesics and forward-backward stochastic differential equations on Lie groups. Conference Publications, 2013, 2013 (special) : 115-121. doi: 10.3934/proc.2013.2013.115

[7]

Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Optimal control problems of forward-backward stochastic Volterra integral equations. Mathematical Control and Related Fields, 2015, 5 (3) : 613-649. doi: 10.3934/mcrf.2015.5.613

[8]

Xiao Ding, Deren Han. A modification of the forward-backward splitting method for maximal monotone mappings. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 295-307. doi: 10.3934/naco.2013.3.295

[9]

Flavia Smarrazzo, Alberto Tesei. Entropy solutions of forward-backward parabolic equations with Devonshire free energy. Networks and Heterogeneous Media, 2012, 7 (4) : 941-966. doi: 10.3934/nhm.2012.7.941

[10]

Andrés Contreras, Juan Peypouquet. Forward-backward approximation of nonlinear semigroups in finite and infinite horizon. Communications on Pure and Applied Analysis, 2021, 20 (5) : 1893-1906. doi: 10.3934/cpaa.2021051

[11]

Jiongmin Yong. Forward-backward stochastic differential equations: Initiation, development and beyond. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022011

[12]

Fabio Paronetto. A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class. Discrete and Continuous Dynamical Systems - S, 2017, 10 (4) : 853-866. doi: 10.3934/dcdss.2017043

[13]

Flavia Smarrazzo, Andrea Terracina. Sobolev approximation for two-phase solutions of forward-backward parabolic problems. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1657-1697. doi: 10.3934/dcds.2013.33.1657

[14]

Yu Fu, Weidong Zhao, Tao Zhou. Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs. Discrete and Continuous Dynamical Systems - B, 2017, 22 (9) : 3439-3458. doi: 10.3934/dcdsb.2017174

[15]

Jie Xiong, Shuaiqi Zhang, Yi Zhuang. A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance. Mathematical Control and Related Fields, 2019, 9 (2) : 257-276. doi: 10.3934/mcrf.2019013

[16]

Adel Chala, Dahbia Hafayed. On stochastic maximum principle for risk-sensitive of fully coupled forward-backward stochastic control of mean-field type with application. Evolution Equations and Control Theory, 2020, 9 (3) : 817-843. doi: 10.3934/eect.2020035

[17]

Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2543-2557. doi: 10.3934/dcds.2020374

[18]

Dariusz Borkowski. Forward and backward filtering based on backward stochastic differential equations. Inverse Problems and Imaging, 2016, 10 (2) : 305-325. doi: 10.3934/ipi.2016002

[19]

Derdei Mahamat Bichara. Effects of migration on vector-borne diseases with forward and backward stage progression. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 6297-6323. doi: 10.3934/dcdsb.2019140

[20]

Lianzhang Bao, Zhengfang Zhou. Traveling wave in backward and forward parabolic equations from population dynamics. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1507-1522. doi: 10.3934/dcdsb.2014.19.1507

2020 Impact Factor: 1.327

Metrics

  • PDF downloads (187)
  • HTML views (0)
  • Cited by (24)

Other articles
by authors

[Back to Top]