Generalized fractional Lévy processes with fractional Brownian motion limit and applications to stochastic volatility models

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Arbitrage in Fractal Modulated Markets When the Volatility is Stochastic

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...

Stochastic integrals and conditional full support

We give a simple criterion for a stochastic process Z := H+K ·W , where H and K are respectively continuous and left-continuous processes independent of the driving Brownian motion W , which ensures that Z has the conditional full support property, introduced by Guasoni, Rásonyi, and Schachermayer, in connection to pricing models with transaction costs. As an application of this result, we show...

Generalized Fractional Master Equation for Self-Similar Stochastic Processes Modelling Anomalous Diffusion

The Master Equation approach to model anomalous diffusion is considered. Anomalous diffusion in complex media can be described as the result of a superposition mechanism reflecting inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equatio...