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The Skorokhod embedding problem and its offspring. (English) Zbl 1189.60088

Summary: 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, based on one-dimensional potential theory, is made. Some new facts which appeared in a natural way when different solutions were cross-examined, are reported. Azéma and Yor’s and Root’s solutions are studied extensively. A possible use of the latter is suggested together with a conjecture.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60G44 Martingales with continuous parameter
60J25 Continuous-time Markov processes on general state spaces
60J45 Probabilistic potential theory
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
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