Abstract
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 timereversal argument. This approach allows us to address the longstanding question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the nmarginal 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 onemarginal Root case. Our results hold for general, onedimensional, martingale diffusions.
Original language  English 

Pages (fromto)  211259 
Number of pages  49 
Journal  Probability Theory and Related Fields 
Volume  173 
Issue number  12 
Early online date  10 Feb 2018 
DOIs  
Publication status  Published  28 Feb 2019 
ASJC Scopus subject areas
 Analysis
 Statistics and Probability
 Statistics, Probability and Uncertainty
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Alex Cox
 Department of Mathematical Sciences  Deputy Head of Department
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Probability Laboratory at Bath
Person: Research & Teaching