Customized tamed numerical schemes for SDEs and BSDEs

In this talk we introduce a family of numerical approximations for the stochastic differentialequations (SDEs) with, possibly, no-globally Lipschitz coefficients. We show that for a given Lyapunovfunction V : R → [1,∞) we can construct a suitably tamed Euler scheme that preserves so calledV-stability property of the original SDEs without imposing any restrictions on the time discretisationstep. V-stability condition plays a crucial role in numerous stability and integrability results for SDEsdeveloped by Khasminski [1]. These results have important consequences for MLMC simulationswhere it is important that the numerical scheme preserves qualitative properties of the solutions tothe SDEs for all range of time-steps. We will further show that developed methodology naturallyextends to the time-discretizations of backward SDEs (BSDEs). References[1] R.Z. Khasminski. Stochastic Stability of Differential Equations. Kluwer Academic Pub, 1980. ∗School of Mathematics University of Edinburgh, ([email protected]).