On the Root solution to the Skorokhod embedding problem given full marginals

Alexandre Richard (1, 2) , Xiaolu Tan (3) , Nizar Touzi (4)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

This paper examines the Root solution of the Skorohod embedding problem given full marginals on some compact time interval. Our results are obtained by limiting arguments based on finitely-many marginals Root solution of Cox, Oblój, and Touzi. Our main result provides a characterization of the corresponding potential function by means of a convenient parabolic PDE.

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Alexandre Richard, Xiaolu Tan, Nizar Touzi. On the Root solution to the Skorokhod embedding problem given full marginals. 2018. ⟨hal-01902839v1⟩