The maximum maximum of a martingale constrained by an intermediate law
成果类型：
Article
署名作者：
Brown, H; Hobson, D; Rogers, LCG
署名单位：
University of Bath
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/PL00008771
发表日期：
2001
页码：
558-578
关键词：
摘要：
Let (M-t) be any martingale with M-0 = 0, an intermediate law M-1 similar to mu (1), and terminal law M-2 similar to mu (2), and let (M) over bar (2) = sup(0 less than or equal to1 less than or equal to2) M-t. In this paper we prove that there exists an upper bound, with respect to stochastic ordering of probability measures, on the law of (M) over bar (2). We construct, using excursion theory, a martingale which attains this maximum. Finally we apply this result to the robust hedging of a lookback option.
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