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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 83 Issue: 12
  • Publication Date: 2013
  • Doi Number: 10.1016/j.spl.2013.09.008
  • Journal Name: STATISTICS & PROBABILITY LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2729-2734
  • Keywords: Maximum drawdown, Maximum loss, Fractional Brownian motion, Large deviation, Gaussian process, DRAWDOWN, SUPREMUM
  • Middle East Technical University Affiliated: No

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.