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Stochastic grid bundling method for backward stochastic differential equations
In this work, we apply the Stochastic Grid Bundling Method (SGBM) to
numerically solve backward stochastic differential equations (BSDEs). The SGBM
algorithm is based on conditional expectations approximation by means of
bundling of Monte Carlo sample paths and a local regress-later regression
within each bundle. The basic algorithm for solving the backward stochastic
differential equations will be introduced and an upper error bound is
established for the local regression. A full error analysis is also conducted
for the explicit version of our algorithm and numerical experiments are
performed to demonstrate various properties of our algorithm