Limiting Distribution of the Maximum Drawdown for Brownian Motion with Positive Drift
The maximum drawdown of a stochastic process is the largest peak-to-troughdecline observed over a given horizon [0, T]. Using arguments from extremevalue theory, we derive the limiting distribution of the maximum drawdown fora Brownian motion with positive drift as T → ∞. We show that, after suitablecentering and scaling, the maximum drawdown converges in distribution to theGumbel law.
