A Posteriori Estimates for Backward SDEs

Suppose an approximation to the solution of a backward SDE is precomputed by some numerical algorithm. In this paper we provide a posteriori estimates on the $L^2$-approximation error between true solution and approximate solution. These a posteriori estimates provide upper and lower bounds for the approximation error. They can be expressed solely in terms of the approximate solution and the data of the backward SDE, and can be estimated consistently by simulation in typical situations. We also illustrate by some numerical experiments in the context of least-squares Monte Carlo how the a posteriori estimates can be applied in practice.