The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach
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 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.
Keywords
Cite
@article{arxiv.1505.03169,
title = {The Root solution to the multi-marginal embedding problem: an optimal stopping and time-reversal approach},
author = {Alexander M. G. Cox and Jan Obłój and Nizar Touzi},
journal= {arXiv preprint arXiv:1505.03169},
year = {2017}
}
Comments
37 pages, 6 figures. Revised version, to include martingale diffusions, and other improvements