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On the Integral of the Fractional Brownian Motion and Some Pseudo-Fractional Gaussian Processes
Mathematics, 2019 We investigate the main statistical parameters of the integral over time of the fractional Brownian motion and of a kind of pseudo-fractional Gaussian process, obtained as a classical Gauss−Markov process from Doob representation by replacing ...
Mario Abundo, Enrica Pirozzi
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Arbitrage with Fractional Brownian Motion [PDF]
Mathematical Finance, 1997 Fractional Brownian motion has been suggested as a model for the movement of log share prices which would allow long–range dependence between returns on different days. While this is true, it also allows arbitrage opportunities, which we demonstrate both indirectly and by constructing such an arbitrage.
exaly +3 more sources
Stochastic integration for tempered fractional Brownian motion [PDF]
Stochastic Processes and Their Applications, 2014 Mark Meerschaert, Farzad Sabzikar
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Fractional Brownian Motion [PDF]
, 2019 There are natural phenomena in which wide variability is commonly observed, most notably the weather. Any expectations of regularity, or independence of this year’s weather from the past or the future, are not borne out by tradition or folklore. Mandelbrot and Wallis [16.1] saw the essence of traditional knowledge expressed in the Old Testament ...
Oksana Banna +3 more
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Mathematics, 2021 Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to ...
Ying Chang, Yiming Wang, Sumei Zhang
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Multiscale Volatility Analysis for Noisy High-Frequency Prices
Risks, 2023 We present a multiscale analysis of the volatility of intraday prices from high-frequency data. Our multiscale framework includes a fractional Brownian motion and microstructure noise as the building blocks.
Tim Leung, Theodore Zhao
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Asymptotic Normality of Parameter Estimators for~Mixed Fractional Brownian Motion with Trend
Austrian Journal of Statistics, 2023 We investigate the mixed fractional Brownian motion of the form Xt = θt+σWt +κBtH , driven by a standard Brownian motion W and a fractional Brownian motion B H with Hurst parameter H.
Kostiantyn Ralchenko, Mykyta Yakovliev
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Pricing European Options under a Fuzzy Mixed Weighted Fractional Brownian Motion Model with Jumps
Fractal and Fractional, 2023 This study investigates the pricing formula for European options when the underlying asset follows a fuzzy mixed weighted fractional Brownian motion within a jump environment.
Feng Xu, Xiao-Jun Yang
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Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions
Jurnal Matematika Integratif, 2020 The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others.
Herry Pribawanto Suryawan
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Fractal Stochastic Processes on Thin Cantor-Like Sets
Mathematics, 2021 We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with
Alireza Khalili Golmankhaneh +1 more
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