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Two discretizations of a class of locally Lipschitz Markovian backwardstochastic differential equations (BSDEs) are studied. The first is theclassical Euler scheme which approximates a projection of the processes Z, andthe second a novel scheme based on Malliavin weights which approximates themariginals of the process Z directly. Extending the representation theorem ofMa and Zhang leads to advanced a priori estimates and stability results forthis class of BSDEs. These estimates are then used to obtain competitiveconvergence rates for both schemes with respect to the number of points in thetime-grid. The class of BSDEs considered includes Lipschitz BSDEs withfractionally smooth terminal condition as well as quadratic BSDEs with bounded,H\"older continuous terminal condition (for bounded, differentiablevolatility), and BSDEs related to proxy methods in numerical analysis.

Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions