Model-independent pricing with insider information: a skorokhod embedding approach

The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices

This set of lecture notes is concerned with the following pair of ideas and concepts: 1) The Skorokhod Embedding problem (SEP) is, given a stochastic process X = (Xt)t≥0 and a measure μ on the state space of X, to find a stopping time τ such that the stopped process Xτ has law μ. Most often we take the process X to be Brownian motion, and μ to be a centred probability measure. 2) The standard a...

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...

An Optimal Skorokhod Embedding for Di usionsA

An Optimal Skorokhod Embedding for Diffusions

Given a Brownian motion (Bt)t≥0 and a general target law μ (not necessarily centred or even in L) we show how to construct an embedding of μ in B. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of μ. The embedding is then...

Optimal Skorokhod embedding under nitely-many

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...