Drawdown and Drawup for Fractional Brownian Motion with Trend

Long Bai, Peng Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We consider the drawdown and drawup of a fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in a financial market. We derive the asymptotics of tail probabilities of the maximum drawdown and maximum drawup, respectively, as the threshold goes to infinity. It turns out that the extremes of drawdown lead to new scenarios of asymptotics depending on the Hurst index of fractional Brownian motion.

Original languageEnglish
Pages (from-to)1581-1612
Number of pages32
JournalJournal of Theoretical Probability
Issue number3
Publication statusPublished - 1 Sept 2019
Externally publishedYes


  • Drawdown
  • Drawup
  • Fractional Brownian motion
  • Geometric fractional Brownian motion
  • Pickands constant
  • Piterbarg constant


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