Optimal Skorokhod embedding given full marginals and Azéma -Yor peacocks *

Sigrid Källblad (1) , Xiaolu Tan (2) , Nizar Touzi (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0, 1]. The problem is related to the study of extremal martingales associated with a peacock (" process increasing in convex order " , by Hirsch, Profeta, Roynette and Yor [16]). A general duality result is obtained by convergence techniques. We then study the case where the reward function depends on the maximum of the embedding process, which is the limit of the martingale transport problem studied in Henry-Labord ere, Ob lój , Spoida and Touzi [13]. Under technical conditions, some explicit characteristics of the solutions to the optimal SEP as well as to its dual problem are obtained. We also discuss the associated martingale inequality.

Mots clés: Skorokhod embedding problem; peacocks; martingale inequality; mar-tingale transport problem; maximum of martingale given marginals

Domaines: Probabilités [math.PR]

Sigrid Källblad, Xiaolu Tan, Nizar Touzi. Optimal Skorokhod embedding given full marginals and Azéma -Yor peacocks *. The Annals of Applied Probability, 2016. ⟨hal-01247001⟩