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Fractional calculus and continuous-time finance

journal contribution
posted on 2023-06-08, 18:27 authored by Enrico Scalas, Rudolf Gorenflo, Francesco Mainardi
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.

History

Publication status

  • Published

Journal

Physica A: Statistical Mechanics and its Applications

ISSN

0378-4371

Publisher

Elsevier

Issue

1-4

Volume

284

Page range

376-384

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-10-02

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