Simulation of BSDEs by Wiener chaos expansion
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.
backward stochastic differential equations
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