High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control
Year: 2017
Communications in Computational Physics, Vol. 21 (2017), Iss. 3 : pp. 808–834
Abstract
This is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve the second-order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler method is used to discretize the forward SDE, which dramatically reduces the entire computational complexity. Moreover, it is shown that the usual quantities of interest (e.g., the solution tuple ($Y_t$,$Z_t$,$A_t$,$Γ_t$) of the 2FBSDEs) are still of high order accuracy. Several numerical examples are given to show the effectiveness of the proposed numerical schemes. Applications of our numerical schemes to stochastic optimal control problems are also presented.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0056
Communications in Computational Physics, Vol. 21 (2017), Iss. 3 : pp. 808–834
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
-
Explicit multistep stochastic characteristic approximation methods for forward backward stochastic differential equations
Liu, Ying | Sun, Yabing | Zhao, WeidongDiscrete & Continuous Dynamical Systems - S, Vol. 15 (2022), Iss. 4 P.773
https://doi.org/10.3934/dcdss.2021044 [Citations: 1] -
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
Beck, Christian | E, Weinan | Jentzen, ArnulfJournal of Nonlinear Science, Vol. 29 (2019), Iss. 4 P.1563
https://doi.org/10.1007/s00332-018-9525-3 [Citations: 174] -
An Efficient Gradient Projection Method for Stochastic Optimal Control Problems
Gong, Bo | Liu, Wenbin | Tang, Tao | Zhao, Weidong | Zhou, TaoSIAM Journal on Numerical Analysis, Vol. 55 (2017), Iss. 6 P.2982
https://doi.org/10.1137/17M1123559 [Citations: 20] -
An explicit second-order numerical scheme for mean-field forward backward stochastic differential equations
Sun, Yabing | Zhao, WeidongNumerical Algorithms, Vol. 84 (2020), Iss. 1 P.253
https://doi.org/10.1007/s11075-019-00754-2 [Citations: 4] -
A multi-step scheme based on cubic spline for solving backward stochastic differential equations
Teng, Long | Lapitckii, Aleksandr | Günther, MichaelApplied Numerical Mathematics, Vol. 150 (2020), Iss. P.117
https://doi.org/10.1016/j.apnum.2019.09.016 [Citations: 11] -
Convergence Analysis for an Online Data-Driven Feedback Control Algorithm
Liang, Siming | Sun, Hui | Archibald, Richard | Bao, FengMathematics, Vol. 12 (2024), Iss. 16 P.2584
https://doi.org/10.3390/math12162584 [Citations: 0] -
Numerical methods for backward stochastic differential equations: A survey
Chessari, Jared | Kawai, Reiichiro | Shinozaki, Yuji | Yamada, ToshihiroProbability Surveys, Vol. 20 (2023), Iss. none
https://doi.org/10.1214/23-PS18 [Citations: 8] -
An efficient third-order scheme for BSDEs based on nonequidistant difference scheme
Pak, Chol-Kyu | Kim, Mun-Chol | Rim, Chang-HoNumerical Algorithms, Vol. 85 (2020), Iss. 2 P.467
https://doi.org/10.1007/s11075-019-00822-7 [Citations: 2] -
Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs
Fu, Yu | Zhao, Weidong | Zhou, TaoDiscrete & Continuous Dynamical Systems - B, Vol. 22 (2017), Iss. 9 P.3439
https://doi.org/10.3934/dcdsb.2017174 [Citations: 12] -
A high-order numerical scheme for stochastic optimal control problem
Li, Yunzhang
Journal of Computational and Applied Mathematics, Vol. 427 (2023), Iss. P.115158
https://doi.org/10.1016/j.cam.2023.115158 [Citations: 0] -
Explicit Deferred Correction Methods for Second-Order Forward Backward Stochastic Differential Equations
Yang, Jie | Zhao, Weidong | Zhou, TaoJournal of Scientific Computing, Vol. 79 (2019), Iss. 3 P.1409
https://doi.org/10.1007/s10915-018-00896-w [Citations: 6] -
A Unified Probabilistic Discretization Scheme for FBSDEs: Stability, Consistency, and Convergence Analysis
Yang, Jie | Zhao, Weidong | Zhou, TaoSIAM Journal on Numerical Analysis, Vol. 58 (2020), Iss. 4 P.2351
https://doi.org/10.1137/19M1260177 [Citations: 5] -
Explicit theta-Schemes for Mean-Field Backward Stochastic Differential Equations
Sun, Yabing | Zhao, Weidong | Zhou, TaoSIAM Journal on Numerical Analysis, Vol. 56 (2018), Iss. 4 P.2672
https://doi.org/10.1137/17M1161944 [Citations: 10] -
Discretization of a Distributed Optimal Control Problem with a Stochastic Parabolic Equation Driven by Multiplicative Noise
Li, Binjie | Zhou, QinJournal of Scientific Computing, Vol. 87 (2021), Iss. 3
https://doi.org/10.1007/s10915-021-01480-5 [Citations: 6] -
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
Darbon, Jérôme | Meng, TingweiJournal of Computational Physics, Vol. 425 (2021), Iss. P.109907
https://doi.org/10.1016/j.jcp.2020.109907 [Citations: 35] -
Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations
Sun, Yabing | Yang, Jie | Zhao, WeidongNumerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 4 P.798
https://doi.org/10.4208/nmtma.2017.0007 [Citations: 4] -
A Novel High Dimensional Fitted Scheme for Stochastic Optimal Control Problems
Dleuna Nyoumbi, Christelle | Tambue, AntoineComputational Economics, Vol. 61 (2023), Iss. 1 P.1
https://doi.org/10.1007/s10614-021-10197-4 [Citations: 1]