scholarly journals Malliavin calculus for backward stochastic differential equations and application to numerical solutions

2011 ◽  
Vol 21 (6) ◽  
pp. 2379-2423 ◽  
Author(s):  
Yaozhong Hu ◽  
David Nualart ◽  
Xiaoming Song
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Malliavin Calculus ◽  
Numerical Solutions ◽  
Backward Stochastic Differential Equations

scholarly journals A regression-based Monte Carlo method to solve two-dimensional forward backward stochastic differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaofei Li ◽  
Yi Wu ◽  
Quanxin Zhu ◽  
Songbo Hu ◽  
Chuan Qin
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Solutions ◽  
Backward Stochastic Differential Equations ◽  
Characteristic Functions ◽  
Two Dimensional ◽  
Least Squares Regression ◽  
European Option Pricing

AbstractThe purpose of this paper is to investigate the numerical solutions to two-dimensional forward backward stochastic differential equations(FBSDEs). Based on the Fourier cos-cos transform, the approximations of conditional expectations and their errors are studied with conditional characteristic functions. A new numerical scheme is proposed by using the least-squares regression-based Monte Carlo method to solve the initial value of FBSDEs. Finally, a numerical experiment in European option pricing is implemented to test the efficiency and stability of this scheme.

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