A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations

被引：39
|
作者：
Zhao, Weidong [1 ]
Zhang, Wei [1 ]
Ju, Lili [2 ,3 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[2] Univ S Carolina, Dept Math, Columbia, SC 29208 USA
[3] Beijing Computat Sci Res Ctr, Beijing 100084, Peoples R China
来源：
COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2014年 / 15卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Decoupled forward-backward stochastic differential equations; numerical scheme; error estimates; DISCRETE-TIME APPROXIMATION; THETA-SCHEME; DISCRETIZATION;
D O I：
10.4208/cicp.280113.190813a
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed method under general situations. Then we present error estimates for each of the specific cases when some classical numerical schemes for solving the forward SDE are taken in the method; in particular, we prove that the proposed method is second-order accurate if used together with the order-2.0 weak Taylor scheme for the SDE. Some examples are also given to numerically demonstrate the accuracy of the proposed method and verify the theoretical results.
引用
收藏
页码：618 / 646
页数：29
相关论文
共 50 条
  • [41] On the robustness of backward stochastic differential equations
    Briand, P
    Delyon, B
    Mémin, J
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 97 (02) : 229 - 253
  • [42] SINC-? SCHEMES FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
    Wang, Xu
    Zhao, Weidong
    Zhou, Tao
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2022, 60 (04) : 1799 - 1823
  • [43] Error estimates of finite element methods for nonlinear fractional stochastic differential equations
    Zhang, Yanpeng
    Yang, Xiaoyuan
    Li, Xiaocui
    ADVANCES IN DIFFERENCE EQUATIONS, 2018,
  • [44] Error estimates of finite element methods for nonlinear fractional stochastic differential equations
    Yanpeng Zhang
    Xiaoyuan Yang
    Xiaocui Li
    Advances in Difference Equations, 2018
  • [45] A new numerical method for 1-D backward stochastic differential equations without using conditional expectations
    Sghir, Aissa
    Hadiri, Soukaina
    RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2020, 28 (02) : 79 - 91
  • [46] Stability of backward stochastic differential equations: the general Lipschitz case
    Papapantoleon, Antonis
    Possamai, Dylan
    Saplaouras, Alexandros
    ELECTRONIC JOURNAL OF PROBABILITY, 2023, 28
  • [47] A First Order Scheme for Backward Doubly Stochastic Differential Equations
    Bao, Feng
    Cao, Yanzhao
    Meir, Amnon
    Zhao, Weidong
    SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2016, 4 (01): : 413 - 445
  • [48] A Fully Discrete Explicit Multistep Scheme for Solving Coupled Forward Backward Stochastic Differential Equations
    Liu, Ying
    Sun, Yabing
    Zhao, Weidong
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2020, 12 (03) : 643 - 663
  • [49] Numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers
    Xu, Mingyu
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 236 (06) : 1137 - 1154
  • [50] MEAN-SQUARE CONVERGENCE OF NUMERICAL APPROXIMATIONS FOR A CLASS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
    Chen, Chuchu
    Hong, Jialin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (08): : 2051 - 2067
12345