The Skorokhod embedding problem and its offspring

By Jan Obłój. 2004

273 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fa6669083d44855b5172bb306b96da825f227b5d

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Mathematical Physics

Citations in the corpus

Optimal Skorokhod embedding given full marginals and Azema-Yor peacocks (2015, background): “This approach is based on the fact that any continuous martingale can be viewed as a timechanged Brownian motion; let us refer to the survey paper of Ob lój [27] and Hobson [19].”
Complete Duality for Martingale Optimal Transport on the Line (2015, background): “Keywords Martingale Optimal Transport; Kantorovich Duality AMS 2010 Subject Classification 60G42; 49N05”
The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, methodology): “For sufficiency, an explicit model can be constructed using techniques of Skorokhod embeddings, see Ob lój [31].”
Universality of the asymptotics of the one-sided exit problem for integrated processes (2010, unknown): “Moreover, by the Burkholder– Davis–Gundy (BDG) inequality (see the version in [28], Proposition 2.”
Structure of optimal martingale transport plans in general dimensions (2015, background): “Note that the one-dimensional case is closely related to Skorohod embedding problems [27], since real valued martingales can be realized as adequately stopped Brownian paths.”
The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices (2011, methodology): “Existing solutions to the SEP (see Oblój [43] for a comprehensive survey) can be used to give bounds on the prices of financial options; conversely questions about the range of no-arbitrage prices for path-dependent options motivates the search for further solutions of the SEP.”
A new approach to strong embeddings (2007, background): “For a detailed account of these activities, see the comprehensive recent survey of Obłój [16] and the bibliography of the monograph by Csörgő and Révész [6].”
Adapted Wasserstein distances and stability in mathematical finance (2019, background): “Following the publication of Hobson’s seminal article [35] connections with the Skorokhod embedding problem have been a driving force of the field, see the surveys of Hobson [36] and Ob lój [47].”
Optimal transportation under controlled stochastic dynamics (2013, background): “In Davis, Obloj and Raval [14], the authors consider a similar problem for the weighted variance swap option which can be included in our context.”
Root's barrier: Construction, optimality and applications to variance options. (2011, background): “For a comprehensive survey of the literature on the Skorokhod embedding problem, we refer the reader to Ob lój [27].”
On a problem of optimal transport under marginal martingale constraints (2012, methodology): “Arguably, the most important tool in model-independent finance is the Skorokhod-embedding approach; an extensive overview is given by Obłój in [23].”
Size bias for one and all (2013, background): “The excellent survey by Ob lój [67] should be consulted for the history and connections to the potential of a measure.”
Martingale optimal transport and robust hedging in continuous time (2012, methodology): “We refer the reader to the excellent survey of Hobson [23] for robust hedging and to Obłój [34] for the Skorokhod embedding problem.”
An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, unknown): “We also refer to the survey papers by Oblój [63] and Hobson [45] for more details.”
Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity (2008, unknown): “The main idea of the proof of Theorem 2 was to introduce a dummy random vector � independent of �. However, the independence property is stronger than what we really need in the proof of Theorem 2. Below we come to a weaker condition invoking a version of the Skorokhod embedding (a detailed survey o”