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In this paper, we consider the drawdown and drawup of the fractional Brownianmotion with trend, which corresponds to the logarithm of geometric fractionalBrownian motion representing the stock price in financial market. We derive theasymptotics of tail probabilities of the maximum drawdown and maximum drawup asthe threshold goes to infinity, respectively. It turns out that the extremes ofdrawdown leads to new scenarios of asymptotics depending on Hurst index offractional Brownian motion.

Drawdown and drawup for fractional Brownian motion with trend