2015/09/21 by Nikolai Dokuchaev, Dokuchaev, Nikolai · 1 citation
Economics, Econometrics and Finance · Mathematics · #60G22 #91G10 #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60G22 #msc:91G10
paper · pdf · doi:10.48550/arxiv.1509.06112
openalex publication_date 2015/09/21 · arxiv created 2015/10/13 · arxiv updated 2015/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider fractional Brownian motion with the Hurst parameters from (1/2,1). We found that the increment of a fractional Brownian motion can be represented as the sum of a two independent Gaussian processes one of which is smooth in the sense that it is differentiable in mean square. We consider fractional Brownian motion and stochastic integrals generated by the Riemann sums. As an example of applications, this results is used to find an optimal pre-programmed strategy in the mean-variance setting for a Bachelier type market model driven by a fractional Brownian motion.