Abstract
We solve Skorokhod's embedding problem for Brownian motion with linear drift (Wt + κ t)t≥0 by means of techniques of stochastic control theory. The search for a stopping time T such that the law of WT + κ T 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 [3] of the classical version of Skorokhod's embedding problem using martingale representation techniques.
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