Abstract.
Let (M t ) be any martingale with M 0≡ 0, an intermediate law M 1∼μ1, and terminal law M 2∼μ2, and let M¯ 2≡ sup0≤ t ≤2 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¯ 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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Received: 26 December 1998 / Revised version: 20 April 2000 /¶Published online: 15 February 2001
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Brown, H., Hobson, D. & Rogers, L. The maximum maximum of a martingale constrained by an intermediate law. Probab Theory Relat Fields 119, 558–578 (2001). https://doi.org/10.1007/PL00008771
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DOI: https://doi.org/10.1007/PL00008771