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The maximum maximum of a martingale constrained by an intermediate law
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  • Published: April 2001

The maximum maximum of a martingale constrained by an intermediate law

  • Haydyn Brown1,
  • David Hobson1 &
  • L.C.G. Rogers1 

Probability Theory and Related Fields volume 119, pages 558–578 (2001)Cite this article

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY. UK. e-mail: dgh@maths.bath.ac.uk, , , , , , GB

    Haydyn Brown, David Hobson & L.C.G. Rogers

Authors
  1. Haydyn Brown
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  2. David Hobson
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  3. L.C.G. Rogers
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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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  • Issue Date: April 2001

  • DOI: https://doi.org/10.1007/PL00008771

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  • Mathematics Subject Classification (2000): 60G40, 60G44
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