Abstract
In this talk we introduce a family of explicit numerical approximations for the forward backward stochastic differential equations (FBSDEs) with, possibly, no-globally Lipschitz coefficients. We will first focus on the forward process. We show that for a given Lyapunov function V:R^d ->[1,infty) we can construct a suitably tamed Euler scheme that preserves so called V-stability property of the original SDEs. V-stability condition plays a crucial role in numerous stability and integrability results for SDEs developed by Khasminski. We will further show that developed methodology naturally extends to the time-discretizations of BSDEs. We show that newly developed methodology allows to analyse BSDEs with drivers having polynomial growth and that are also monotone in the state variable. Proposed schemes preserve qualitative properties of the solutions to the FBSDEs for all ranges of time-steps.