2013/02/08 by Ceren Vardar, Vardar, Ceren, Hatice Çakar +1
Economics, Econometrics and Finance · #60G15 #60G22 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1302.2019
openalex publication_date 2013/02/08 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
In this study, it is theoretically proven that the expected value of maximum\nloss of fractional Brownian motion (fBm) up to time 1 with Hurst parameter\n[1/2,1) is bounded above by 2/\√(\π) and below by 1/\√(\π). This\nresult is generalized for fBm with H\∈[1/2,1) up to any fixed time, t.\nThis also leads us to the bounds related to the distribution of maximum loss of\nfBm. As numerical study some lower bounds on the expected value of maximum loss\nof fBm up to time 1 are obtained by discretization. Simulation study is\nconducted with Cholesky method. Finally, comparison of the established bounds\nwith simulation results is given.\n