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The maximum maximum of a martingale

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1686)

Abstract

Let (M t )0≤t≤1 be any martingale with initial law M 0 ~ μ0 and terminal law M 1 ~ μ1 and let S≡sup0≤t≤1 M t . Then there is an upper bound, with respect to stochastic ordering of probability measures, on the law of S.

An explicit description of the upper bound is given, along with a martingale whose maximum attains the upper bound.

Keywords

  • Brownian Motion
  • Probability Measure
  • Call Option
  • Contingent Claim
  • Continuous Martingale

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1998 Springer-Verlag

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Hobson, D.G. (1998). The maximum maximum of a martingale. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds) Séminaire de Probabilités XXXII. Lecture Notes in Mathematics, vol 1686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101762

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  • DOI: https://doi.org/10.1007/BFb0101762

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

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