New and refined bounds for expected maxima of fractional Brownian motion

2016/12/23 by Konstantin Borovkov, Yuliya Mishura, Borovkov, Konstantin +5
Decision Sciences · Economics, Econometrics and Finance · #60E15 #60G15 #60G22 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1612.07842

openalex publication_date 2016/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For the fractional Brownian motion B^H with the Hurst parameter value H in (0,1/2), we derive new upper and lower bounds for the difference between the expectations of the maximum of B^H over [0,1] and the maximum of B^H over the discrete set of values in^-1, i=1,…, n. We use these results to improve our earlier upper bounds for the expectation of the maximum of B^H over [0,1] and derive new upper bounds for Pickands' constant.

Citations

• An error bound in the Sudakov-Fernique inequality

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