Portfolio optimisation beyond semimartingales: Shadow prices and fractional Brownian motion

Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion∗

While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessarily semimartingales, the existence of an optimal trading strategy for utility m...

Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs

The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrari...

Integration in a Normal World: Fractional Brownian Motion and Beyond

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Lauri Viitasaari Name of the doctoral dissertation Integration in a Normal World: Fractional Brownian Motion and Beyond Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 14/2014 Field of research Mathematics Manuscript submitted 12 ...

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.

Tempered fractional Brownian motion