scholarly journals Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression

Bernoulli ◽  
2016 ◽  
Vol 22 (1) ◽  
pp. 530-562 ◽  
Author(s):  
Emmanuel Gobet ◽  
Plamen Turkedjiev
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Least Squares Regression

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.

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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