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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