scholarly journals A New Second Order Numerical Scheme for Solving Forward Backward Stochastic Differential Equations with Jumps

2016 ◽  
Vol 07 (12) ◽  
pp. 1408-1414
Author(s):  
Hongqiang Zhou ◽  
Yang Li ◽  
Zhe Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Scheme ◽  
Backward Stochastic Differential Equations ◽  
Second Order

An Explicit Second-Order Numerical Scheme to Solve Decoupled Forward Backward Stochastic Equations

2014 ◽  
Vol 4 (4) ◽  
pp. 368-385 ◽  
Author(s):  
Yu Fu ◽  
Weidong Zhao
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
High Accuracy ◽  
Stochastic Equations ◽  
Explicit Scheme ◽  
Second Order ◽  
General Error

AbstractAn explicit numerical scheme is proposed for solving decoupled forward backward stochastic differential equations (FBSDE) represented in integral equation form. A general error inequality is derived for this numerical scheme, which also implies its stability. Error estimates are given based on this inequality, showing that the explicit scheme can be second-order. Some numerical experiments are carried out to illustrate the high accuracy of the proposed scheme.

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.

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