The minimum maximum of a continuous martingale with given initial and terminal laws
成果类型：
Article
署名作者：
Hobson, DG; Pedersen, JL
署名单位：
University of Bath; Swiss Federal Institutes of Technology Domain; ETH Zurich
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2002
页码：
978-999
关键词：
摘要：
Let (M-t)(0less than or equal totless than or equal to1) be a continuous martingale with initial law M-0 similar to mu(0), and terminal law M-1 similar to mu(1), and let S = sup(0less than or equal totless than or equal to1) M-t. In this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of S. We give an explicit construction of this bound. 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.