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The time to a given drawdown in Brownian Motion

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1832)

Abstract

This article deals with optimal stopping of Brownian Motion when the sampling cost is linear in time and the reward upon stopping is a non-decreasing function of the cumulative maximum. This can be viewed as pricing and management of a type of look-back American put option. The case of linear reward function was studied by Dubins & Schwarz [10].

Our treatment of the problem involves a stopped Brownian Motion formula by Taylor (see Taylor [18] and Williams [19]), first exit times by Brownian Motion from open intervals, processes with dichotomous transitions and the Azéma–Yor [2] stopping time.

Keywords

  • Brownian Motion
  • Open Interval
  • Moment Generate Function
  • Exit Time
  • Iterate Logarithm

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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© 2003 Springer-Verlag Berlin Heidelberg

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Meilijson, I. (2003). The time to a given drawdown in Brownian Motion. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVII. Lecture Notes in Mathematics, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40004-2_5

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  • DOI: https://doi.org/10.1007/978-3-540-40004-2_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20520-3

  • Online ISBN: 978-3-540-40004-2

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