A numerical method for solving high-dimensional backward stochastic difference equations using sparse grids

抄録

We propose a numerical method for computing the solutions of high-dimensional Markovian backward stochastic difference equations (BS$\Delta$Es), in which we apply a sparse grid quadrature/interpolation formula. This allows us to calculate the approximated solution accurately and efficiently, which we justify through a rigorous error analysis. Finally, we use a simple numerical experiment to demonstrate the performance of our method.