Drawdown and Drawup for Fractional Brownian Motion with Trend

被引：0
作者：
Long Bai
Peng Liu
机构：
[1] University of Lausanne,Department of Actuarial Science
[2] UNIL-Dorigny,undefined
来源：
Journal of Theoretical Probability | 2019年 / 32卷
关键词：
Drawdown; Drawup; Fractional Brownian motion; Geometric fractional Brownian motion; Pickands constant; Piterbarg constant; Primary 60G15; Secondary 60G70;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：1581 / 1612
页数：31
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