Optimal Skorokhod embedding under nitely-many

Optimal Skorokhod Embedding Under Finitely Many Marginal Constraints

The Skorokhod embedding problem aims to represent a given probability measure on the real line as the distribution of Brownian motion stopped at a chosen stopping time. In this paper, we consider an extension of the optimal Skorokhod embedding problem in Beiglböck, Cox & Huesmann [1] to the case of finitely-many marginal constraints1. Using the classical convex duality approach together with th...

Optimal Transport and Skorokhod Embedding

The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a variety of techniques ranging from excursio...

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

We consider the optimal Skorokhod embedding problem (SEP) given full marginals over the time interval [0, 1]. The problem is related to studying the extremal martingales associated to 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...

An Optimal Skorokhod Embedding for Di usionsA

On the Monotonicity Principle of Optimal Skorokhod Embedding Problem

This is a continuation of our accompanying paper [18]. We provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established in Beiglböck, Cox and Huesmann [2]. Our proof is based on the adaptation of the Monge-Kantorovich duality in our context, a delicate application of the optional cross-section theorem, and a clever conditioning argument intro...