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On the wavelet transform of fractional Brownian motion [PDF]
IEEE Transactions on Information Theory, 1991 A theorem characterizing fractional Brownian motion by the covariance structure of its wavelet transform is established. The authors examine whether there are alternate Gaussian processes whose wavelet transforms have a natural covariance structure.
Jayakumar Ramanathan, Ofer Zeitouni
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Barrier Options and a Reflection Principle of the Fractional Brownian Motion [PDF]
The purpose of this paper is to obtain the price of the barrier options in a fractional Brownian motion environment in the special case of zero interest rate. As a consequence we derive a reflection principle for the fractional Brownian motion.fractional
Cipian Necula
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Winding number of fractional Brownian motion [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 We find the exact winding number distribution of Riemann-Liouville fractional Brownian motion for large times in two dimensions using the propagator of a free particle. The distribution is similar to the Brownian motion case and it is of Cauchy type.
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Risk preference based option pricing in a fractional Brownian market [PDF]
We focus on a preference based approach when pricing options in a market driven by fractional Brownian motion. Within this framework we derive formulae for fractional European options using the traditional idea of conditional expectation.
Rostek, Stefan, Schöbel, Rainer
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Riemann-Stieltjes integrals with respect to fractional Brownian motion and applications [PDF]
, 2010 In this dissertation we study Riemann-Stieltjes integrals with respect to (geometric) fractional Brownian motion, its financial counterpart and its application in estimation of quadratic variation process. From the point of view of financial mathematics,
Azmoodeh, Ehsan
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, 2022 In this article, we introduce a Wong-Zakai type stationary approximation to the fractional Brownian motions and provide a sharp rate of convergence in L-p (Omega). Our stationary approximation is suitable for all values of H is an element of (0, 1).
Viitasaari, Lauri +5 more
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Type I and Type II Fractional Brownian Motions: a Reconsideration [PDF]
The so-called type I and type II fractional Brownian motions are limit distributions associated with the fractional integration model in which pre-sample shocks are either included in the lag structure, or suppressed. There can be substantial differences
James Davidson, Nigar Hashimzade
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Results on the Supremum of Fractional Brownian Motion
, 2009 We show that the distribution of the square of the supremum of reflected fractional Brownian motion up to time a, with Hurst parameter-H greater than 1/2, is related to the distribution of its hitting time to level 1, using the self similarity property of fractional Brownian motion.
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Mixed sub-fractional Brownian motion [PDF]
Random Operators and Stochastic Equations, 2014 Abstract A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional Brownian motion.
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Pricing European and Barrier Options in the Fractional Black-Scholes Market [PDF]
The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5.
Ciprian Necula
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