TY - JOUR

T1 - The Root solution to the multi-marginal embedding problem

T2 - an optimal stopping and time-reversal approach

AU - Cox, Alexander M.G.

AU - Obłój, Jan

AU - Touzi, Nizar

N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/2/4

Y1 - 2019/2/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85041904536&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041904536&partnerID=8YFLogxK

U2 - 10.1007/s00440-018-0833-1

DO - 10.1007/s00440-018-0833-1

M3 - Article

AN - SCOPUS:85041904536

SN - 0178-8051

VL - 173

SP - 211

EP - 259

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -