A linear numerical scheme for nonlinear BSDEs with uniformlycontinuous coefficients

[摘要] We attempt to present a new numerical approach to solve nonlinearbackward stochastic differential equations. First, we present somedefinitions and theorems to obtain the condition,from which we can approximate the nonlinear term of the backwardstochastic differential equation (BSDE) and we get a continuouspiecewise linear BSDE corresponding to the originalBSDE. We use the relationship between backward stochasticdifferential equations and stochastic controls by interpretingBSDEs as some stochastic optimal control problems to solvethe approximated BSDE and we prove that the approximated solution converges to the exact solution of the original nonlinear BSDE.

[学科分类] 应用数学