2008): “A BSDE approach to the Skorokhod embedding problem for the Brownian motion with drift

We solve Skorokhod’s embedding problem for Brownian motion with linear drift (Wt+ κt)t≥0 by means of techniques of stochastic control theory. The search for a stopping time T such that the law of WT + κT coincides with a prescribed law µ possessing the first moment is based on solutions of backward stochastic differential equations of quadratic type. This new approach generalizes an approach by Bass [Bas] of the classical version of Skorokhod’s embedding problem using martingale representation techniques