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The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach
We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing qu...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6394753/ https://www.ncbi.nlm.nih.gov/pubmed/30880857 http://dx.doi.org/10.1007/s00440-018-0833-1 |
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author | Cox, Alexander M. G. Obłój, Jan Touzi, Nizar |
author_facet | Cox, Alexander M. G. Obłój, Jan Touzi, Nizar |
author_sort | Cox, Alexander M. G. |
collection | PubMed |
description | We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time–space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions. |
format | Online Article Text |
id | pubmed-6394753 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-63947532019-03-15 The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach Cox, Alexander M. G. Obłój, Jan Touzi, Nizar Probab Theory Relat Fields Article We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time–space process. The barriers are characterised by means of a recursive sequence of optimal stopping problems. Moreover, we prove that our solution enjoys a global optimality property extending the one-marginal Root case. Our results hold for general, one-dimensional, martingale diffusions. Springer Berlin Heidelberg 2018-02-10 2019 /pmc/articles/PMC6394753/ /pubmed/30880857 http://dx.doi.org/10.1007/s00440-018-0833-1 Text en © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Cox, Alexander M. G. Obłój, Jan Touzi, Nizar The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
title | The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
title_full | The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
title_fullStr | The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
title_full_unstemmed | The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
title_short | The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
title_sort | root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6394753/ https://www.ncbi.nlm.nih.gov/pubmed/30880857 http://dx.doi.org/10.1007/s00440-018-0833-1 |
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