Simulation of BSDEs by Wiener chaos expansion (Q2454405)

The authors consider the numerical approximation of solutions \((Y,Z)\) to real, scalar backward stochastic differential equations of the form \[ Y_t = \xi + \int_t^T f(s,Y_s,Z_s)ds -\int_t^T Z_s \cdot dB_s, \;\;0\leq t\leq T \] with real terminal random variable \(\xi\) and \(B\) being a \(d\)-dimensional Brownian motion. The paper presents a numerical scheme based on Wiener chaos expansion (of finite order) and Picard iteration. In particular, the scheme is a forward scheme calculating the necessary conditional expectations with chaos decomposition formulas; \(Z\) is computed via the Malliavin derivative. The convergence of the algorithm is established under suitable hypotheses, error bounds are computed and numerical experiments are carried out illustrating the theoretical results.