We survey some new progress on the pricing models driven by fractional Brownian motion or mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating...

The aim of this paper is to provide a semimartingale approximation of a fractional stochastic integration. This result leads us to approximate the fractional Black-Scholes model by a model driven by semimartingales, and a European option pricing formula is found. 2000 AMS Classification: 60H05, 65G15, 62P05.

We prove a Donsker type approximation theorem for the fractional Brownian motion in the case H > 1/2. Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black–Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

In this paper two different methods are presented to approximate the solution of the fractional BlackScholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the applic...

In this paper, Laplace homotopy perturbation method, which is combined form of the Laplace transform and the homotopy perturbation method, is employed to obtain a quick and accurate solution to the fractional Black Scholes equation with boundary condition for a European option pricing problem. The Black-Scholes formula is used as a model for valuing European or American call and put options on ...

the used activated carbon was derived from pine-cone and was used for the removal of acid black 1(ab1) and acid blue 113(ab113) dyes. a batch sorption study was carried out in order to obtain optimum isotherm model. the study showed the best fit of the adsorption isotherm data was obtained using the langmuir model for both dyes. the monolayer maximum saturation capacities of ab1 and ab113 dyes ...

We have re-analyzed two EXOSAT Medium Energy observations during part of the 1984 X-ray outburst of the black-hole candidate transient system 4U1630−47. One observation (May 10) shows fast timing properties (on timescales shorter than ∼250 s) typical of those of other black hole candidates in their high states. The power-spectrum shows a power law with index ∼0.7 and fractional rms amplitude (0...

The purpose of this paper is to assess the risk premium a fractional financial lognormal (Black-Scholes or BS) process relative to a non-fractional and complete financial pricing model. While fractional Brownian BS models based on the Duncan and Wicks calculus were shown to define a no arbitrage financial model, this paper claim is that this martingale need not be the pricing martingale. There ...

We construct non-extremal fractional D-brane solutions of type-II string theory at the Z 2 orbifold point of K3. These solutions generalize known extremal fractional-brane solutions and provide further insights into N = 2 supersymmetric gauge theories and dual descriptions thereof. In particular, we find that for these solutions the horizon radius cannot exceed the non-extremal enhançon radius....

For example, investigating the Hamiltonian constraint equation for a black hole with angular momentum we find that, where finite difference solutions require a resolution of 1024×384 (radial×angular) grid points to find a solution of fractional error 10−5 in the ADM mass, a PSC solution achieves the same accuracy with only 12× 4 collocation points. Furthermore, the fractional error is reduced t...