Bounds on the expected value of maximum loss of fractional Brownian motion

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2015-09-01

Author

Vardar Acar, Ceren

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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 values of the expected value of maximum loss of fractional Brownian motion have been provided through the use of Cholesky decomposition. As a consequence of the simulation study, it has been observed that as the Hurst parameter increases, the values of the expected maximum loss of fractional Brownian motion decreases.

Subject Keywords

Cholesky decomposition, Hurst parameter, Fractional Brownian motion, Maximum loss, Sudakov-Fernique inequality

URI

https://hdl.handle.net/11511/45749

Journal

STATISTICS & PROBABILITY LETTERS

DOI

https://doi.org/10.1016/j.spl.2015.05.001

Collections

Department of Statistics, Article

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Citation Formats

C. Vardar Acar, “Bounds on the expected value of maximum loss of fractional Brownian motion,” STATISTICS & PROBABILITY LETTERS, pp. 117–122, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45749.