Fractional calculus and continuous-time finance
Disordered Systems and Neural Networks
2009-10-31 v1 Statistical Finance
Abstract
In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the L\'evy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predictions on the long-time behaviour of the waiting-time probability density are presented. Finally, a general scaling form is given, based on the solution of the fractional diffusion equation.
Cite
@article{arxiv.cond-mat/0001120,
title = {Fractional calculus and continuous-time finance},
author = {Enrico Scalas and Rudolf Gorenflo and Francesco Mainardi},
journal= {arXiv preprint arXiv:cond-mat/0001120},
year = {2009}
}
Comments
11 pages, no figures, LaTeX2e, submitted to Physica A