A regression-based numerical scheme for backward stochastic differential equations

2017 ◽  
Vol 32 (4) ◽  
pp. 1357-1373 ◽  
Author(s):  
Deng Ding ◽  
Xiaofei Li ◽  
Yiqi Liu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Scheme ◽  
Backward Stochastic Differential Equations

A Multistep Scheme for Decoupled Forward-Backward Stochastic Differential Equations

2016 ◽  
Vol 9 (2) ◽  
pp. 262-288 ◽  
Author(s):  
Weidong Zhao ◽  
Wei Zhang ◽  
Lili Ju
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Error Estimate ◽  
Stochastic Differential Equations ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
Backward Stochastic Differential Equations ◽  
Multistep Scheme ◽  
Theoretical Results ◽  
General Error

AbstractUpon a set of backward orthogonal polynomials, we propose a novel multi-step numerical scheme for solving the decoupled forward-backward stochastic differential equations (FBSDEs). Under Lipschtiz conditions on the coefficients of the FBSDEs, we first get a general error estimate result which implies zero-stability of the proposed scheme, and then we further prove that the convergence rate of the scheme can be of high order for Markovian FBSDEs. Some numerical experiments are presented to demonstrate the accuracy of the proposed multi-step scheme and to numerically verify the theoretical results.

Deferred Correction Methods for Forward Backward Stochastic Differential Equations

2017 ◽  
Vol 10 (2) ◽  
pp. 222-242 ◽  
Author(s):  
Tao Tang ◽  
Weidong Zhao ◽  
Tao Zhou
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Scheme ◽  
Classical Method ◽  
Practical Importance ◽  
Backward Stochastic Differential Equations ◽  
Euler Method ◽  
High Order ◽  
Deferred Correction ◽  
Key Features

AbstractThe deferred correction (DC) method is a classical method for solving ordinary differential equations; one of its key features is to iteratively use lower order numerical methods so that high-order numerical scheme can be obtained. The main advantage of the DC approach is its simplicity and robustness. In this paper, the DC idea will be adopted to solve forward backward stochastic differential equations (FBSDEs) which have practical importance in many applications. Noted that it is difficult to design high-order and relatively “clean” numerical schemes for FBSDEs due to the involvement of randomness and the coupling of the FSDEs and BSDEs. This paper will describe how to use the simplest Euler method in each DC step–leading to simple computational complexity–to achieve high order rate of convergence.

Sign in / Sign up

Export Citation Format

Share Document