Distribution of maximum loss of fractional Brownian motion with drift

Date

2013-07-04

Author

Vardar Acar, Ceren

Metadata

Show full item record

Item Usage Stats

79
views

0
downloads

In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion H ≥ 1/2 with 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

Subject Keywords

Maximum drawdown, Maximum loss, Fractional Brownian motion, Large deviation, Gaussian process

URI

https://hdl.handle.net/11511/77049

Journal

Statistics and Probability Letters

Collections

Unclassified, Article

Suggestions

OpenMETU
Core

Distribution of maximum loss of fractional Brownian motion with drift Caglar, Mine; Vardar Acar, Ceren (Elsevier BV, 2013-12) 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.
Bounds on the expected value of maximum loss of fractional Brownian motion Vardar Acar, Ceren (2015-09-01) It has been theoretically proven through present study that the expected value of maximum loss of fractional Brownian motion up to fixed time t with Hurst parameter [1/2, 1) is bounded above by t(H) root pi/2 and below by t(H)/2. These new bounds provide improvement on those bounds which have been previously derived in the literature. In order to search for closer bounds, numerical study is also performed through discretization method and multivariate Gaussian variables have been examined. The simulated val...
RESULTS ON THE SUPREMUM OF FRACTIONAL BROWNIAN MOTION Vardar Acar, Ceren (2011-04-01) We show that the distribution of the square of the supremum of reflected fractional Brownian motion up to time a, with Hurst parameter-H greater than 1/2, is related to the distribution of its hitting time to level 1, using the self similarity property of fractional Brownian motion. It is also proven that the second moment of supremum of reflected fractional Brownian motion up to time a is bounded above by a(2H). Similar relations are obtained for the supremum of fractional Brownian motion with Hurst parame...
Calculation of the Raman frequencies using volume data in various phases of solid nitrogen and benzene Çetinbaş İşeri, Esin; Yurtseven, Hasan Hamit; Department of Physics (2011) In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the four-dimensional spacetime, the fundamental conformal transformations and the Hamiltonian form of general relativity that leads to the ADM formalism, deﬁned for the conserved quantities of the hypersurfaces of the globally-hyperbolic asymptotically flat spacetimes, are recons...
Maximum loss and maximum gain of spectrally negative Levy processes Vardar Acar, Ceren (2017-12-13) The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Lévy process until the passage time of a given level. Their marginal distributions up to an independent exponential time are also provided. The existing formulas for Brownian motion with drift are recovered using the particular scale functions.

Citation Formats

C. Vardar Acar, “Distribution of maximum loss of fractional Brownian motion with drift,” Statistics and Probability Letters, pp. 2729–2734, 2013, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/77049.