TY - JOUR
AU1 - Bai, Long
AU2 - Liu, Peng
AB - 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.
TI - Drawdown and Drawup for Fractional Brownian Motion with Trend
JF - Journal of Theoretical Probability
DO - 10.1007/s10959-018-0836-y
DA - 2018-06-06
UR - https://www.deepdyve.com/lp/springer-journals/drawdown-and-drawup-for-fractional-brownian-motion-with-trend-8NbUS6MRKG
SP - 1581
EP - 1612
VL - 32
IS - 3
DP - DeepDyve