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A BSDE approach to the Skorokhod embedding problem for the Brownian motion with drift
 

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
10099 Berlin
Germany
December 20, 2007
Abstract
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 [3] 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,
60F17.

  

Source: Ankirchner, Stefan - Institut für Angewandte Mathematik, Universität Bonn

 

Collections: Mathematics