Abstract
For backward stochastic differential equations (BSDEs), we construct a fully explicit multi-step time-discretization scheme and prove its stability and convergence rates. To approximate conditional expectations in our scheme, we design a new algorithm based on the multilevel Monte Carlo (MLMC) method. This estimator can achieve a prescribed error ϵ with a computational effort of order ϵ−2. Numerical experiments are given to illustrate the theoretical results of the proposed methods.
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