The minimum maximum of a continuous martingale with given initial and terminal laws
type: Item
instance of: scholarly article
title: The minimum maximum of a continuous martingale with given initial and terminal laws
zbMATH Open document ID: 1016.60047
author: David Hobson
author: Jesper Lund Pedersen
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: Let \((M_t)_{0\leq t\leq 1}\) be a continuous martingale with initial law \(M_0\sim \mu_0\), and terminal law \(M_1\sim \mu_1\), and let \(S=\sup_{0\leq t\leq 1}M_t\). This paper proves that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of \(S\). An explicit construction of this bound is given. Furthermore a martingale is constructed which attains this minimum by solving a Skorokhod embedding problem. The form of this martingale is motivated by a simple picture. The result is applied to the robust hedging of a forward start digital option.
reviewed by: Yuhu Feng
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60G30
zbMATH DE Number: 1906075
zbMATH Keywords: martingale
zbMATH Keywords: Skorokhod embedding problem
zbMATH Keywords: optimal stopping
zbMATH Keywords: option pricing
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1023481014
OpenAlex ID: W2130918614
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DOI: 10.1214/AOP/1023481014
description: scientific article; zbMATH DE number 1906075