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Limiting Distribution of the Maximum Drawdown for Brownian Motion with Positive Drift

Bermin, Hans-Peter and Holm, Magnus (2025) In Working Papers
Abstract
The maximum drawdown of a stochastic process is the largest peak-to-trough
decline observed over a given horizon [0, T]. Using arguments from extreme
value theory, we derive the limiting distribution of the maximum drawdown for
a Brownian motion with positive drift as T → ∞. We show that, after suitable
centering and scaling, the maximum drawdown converges in distribution to the
Gumbel law.
Please use this url to cite or link to this publication:
author
and
publishing date
type
Working paper/Preprint
publication status
published
subject
keywords
maximum drawdown, extreme value theory, asymptotic distribution, J65, G70, G50
in
Working Papers
issue
2025:9
pages
16 pages
language
English
LU publication?
no
id
62419ff0-4329-43d1-9885-82f3eca91879
date added to LUP
2025-11-12 14:06:35
date last changed
2025-11-12 14:06:35
@misc{62419ff0-4329-43d1-9885-82f3eca91879,
  abstract     = {{The maximum drawdown of a stochastic process is the largest peak-to-trough<br/>decline observed over a given horizon [0, T]. Using arguments from extreme<br/>value theory, we derive the limiting distribution of the maximum drawdown for<br/>a Brownian motion with positive drift as T → ∞. We show that, after suitable<br/>centering and scaling, the maximum drawdown converges in distribution to the<br/>Gumbel law.}},
  author       = {{Bermin, Hans-Peter and Holm, Magnus}},
  keywords     = {{maximum drawdown; extreme value theory; asymptotic distribution; J65; G70; G50}},
  language     = {{eng}},
  note         = {{Working Paper}},
  number       = {{2025:9}},
  series       = {{Working Papers}},
  title        = {{Limiting Distribution of the Maximum Drawdown for Brownian Motion with Positive Drift}},
  url          = {{https://lup.lub.lu.se/search/files/232813145/WP25_9.pdf}},
  year         = {{2025}},
}