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 Probability Surveys > Vol. 1 (2004) open journal systems 


The Skorokhod embedding problem and its offspring

Jan Krzysztof Obłój, Universite Pierre et Marie Curie Paris 6, Warsaw University


Abstract
This is a survey about the Skorokhod embedding problem. It presents all known solutions together with their properties and some applications. Some of the solutions are just described, while others are studied in detail and their proofs are presented. A certain unification of proofs, thanks to real potential theory, is made. Some new facts which appeared in a natural way when different solutions were cross-examined, are reported. Azema and Yor's and Root's solutions are studied extensively. A possible use of the latter is suggested together with a conjecture.

AMS 2000 subject classifications: Primary 60G40, 60G44; Secondary 60J25, 60J45.

Keywords: Skorokhod embedding problem, Chacon-Walsh embedding, Azéma-Yor embedding, Root embedding, stopping times, optimal stopping, one-dimensional potential theory.

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Obłój, Jan Krzysztof, The Skorokhod embedding problem and its offspring, Probability Surveys, 1, (2004), 321-392 (electronic).

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