Journal of Applied Mathematics
Volume 2004 (2004), Issue 6, Pages 461-477

A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients

Omid. S. Fard1 and Ali V. Kamyad2

1Department of Mathematics, Damghan University of Basic Sciences, Damghan, Iran
2Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Received 31 January 2004; Revised 23 June 2004

Copyright © 2004 Omid. S. Fard and Ali V. Kamyad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE corresponding to the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.