Bai, Long and Liu, Peng (2019) Drawdown and Drawup for Fractional Brownian Motion with Trend. Journal of Theoretical Probability, 32 (3). pp. 1581-1612. DOI https://doi.org/10.1007/s10959-018-0836-y
Bai, Long and Liu, Peng (2019) Drawdown and Drawup for Fractional Brownian Motion with Trend. Journal of Theoretical Probability, 32 (3). pp. 1581-1612. DOI https://doi.org/10.1007/s10959-018-0836-y
Bai, Long and Liu, Peng (2019) Drawdown and Drawup for Fractional Brownian Motion with Trend. Journal of Theoretical Probability, 32 (3). pp. 1581-1612. DOI https://doi.org/10.1007/s10959-018-0836-y
Abstract
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.
Item Type: | Article |
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Uncontrolled Keywords: | Drawdown; Drawup; Fractional Brownian motion; Geometric fractional Brownian motion; Pickands constant; Piterbarg constant |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 28 Jan 2021 17:45 |
Last Modified: | 16 May 2024 20:27 |
URI: | http://repository.essex.ac.uk/id/eprint/28168 |
Available files
Filename: DrawdownupRe1.pdf