Nonlinear Filtering with Fractional Brownian Motion

Arbitrage with Fractional Brownian Motion

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. Nonetheless, it is possible by looking at a process similar to the fractional Brownian motio...

Arbitrage with Fractional Brownian Motion ?

In recent years fractional Brownian motion has been suggested to replace the classical Brownian motion as driving process in the modelling of many real world phenomena, including stock price modelling. In several papers seemingly contradictory results on the existence or absence of a riskless gain (arbitrage) in such stock models have been stated. This survey tries to clarify this issue by poin...

Non Linear Filtering Theory in Presence of Fractional Brownian Motion

We develop the ltering theory in the case where both the signal and the observation are solutions of some stochastic diierential equation driven by a multiidimensional fractional Brownian motion. We show that the classical approach fails to give a closed equation for the lter and we develop another approach using an auxiliary processsvalued semimartingale which solves theoretically this problem...

Filtering for Linear Systems Driven by Fractional Brownian Motion

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.