Summary: A BSDE approach to the Skorokhod embedding problem for
the Brownian motion with drift
Stefan Ankirchner and Gregor Heyne and Peter Imkeller
Institut f¨ur Mathematik
Humboldt-Universit¨at zu Berlin
Unter den Linden 6
December 20, 2007
We solve Skorokhod's embedding problem for Brownian motion with linear drift (Wt +
t)t0 by means of techniques of stochastic control theory. The search for a stopping time
T such that the law of WT + 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  of the classical version of
Skorokhod's embedding problem using martingale representation techniques.
Key words and phrases: Skorokhod embedding; Brownian motion; diffusion; stopping
time; control theory; BSDE; quadratic growth; Malliavin calculus.
2000 AMS subject classifications: Primary 60G40, 60G44; secondary 60J65, 60F05,