Distribution of maximum loss of fractional Brownian motion with drift


Caglar M., Vardar-Acar C.

STATISTICS & PROBABILITY LETTERS, vol.83, no.12, pp.2729-2734, 2013 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 83 Issue: 12
  • Publication Date: 2013
  • Doi Number: 10.1016/j.spl.2013.09.008
  • Title of Journal : STATISTICS & PROBABILITY LETTERS
  • Page Numbers: pp.2729-2734
  • Keywords: Maximum drawdown, Maximum loss, Fractional Brownian motion, Large deviation, Gaussian process, DRAWDOWN, SUPREMUM

Abstract

In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H >= 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time t. (C) 2013 Elsevier B.V. All rights reserved.