A Regression-Based Numerical Method for Forward-Backward Stochastic Differential Equations

2014 ◽  
Author(s):  
Deng Ding ◽  
Yiqi Liu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Backward Stochastic Differential Equations

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

2014 ◽  
Vol 15 (3) ◽  
pp. 618-646 ◽  
Author(s):  
Weidong Zhao ◽  
Wei Zhang ◽  
Lili Ju
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Error Estimates ◽  
Backward Stochastic Differential Equations ◽  
Second Order ◽  
Numerical Schemes ◽  
Reference Equations ◽  
Taylor Scheme ◽  
Theoretical Results

AbstractIn 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.

A new numerical method for 1-D backward stochastic differential equations without using conditional expectations

2020 ◽  
Vol 28 (2) ◽  
pp. 79-91
Author(s):  
Aissa Sghir ◽  
Sokaina Hadiri
Keyword(s):  
Kalman Filter ◽  
Linear System ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Extended Kalman Filter ◽  
Backward Stochastic Differential Equations ◽  
Conditional Expectations ◽  
Non Linear System ◽  
Reference Trajectories

AbstractIn this paper, we propose a new numerical method for 1-D backward stochastic differential equations (BSDEs for short) without using conditional expectations. The approximations of the solutions are obtained as solutions of a backward linear system generated by the terminal conditions. Our idea is inspired from the extended Kalman filter to non-linear system models by using a linear approximation around deterministic nominal reference trajectories.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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