Fractional calculus and continuous-time finance

Scalas, Enrico, Gorenflo, Rudolf and Mainardi, Francesco (2000) Fractional calculus and continuous-time finance. Physica A: Statistical Mechanics and its Applications, 284 (1-4). pp. 376-384. ISSN 0378-4371

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Enrico Scalas
Date Deposited: 02 Oct 2014 11:20
Last Modified: 02 Oct 2014 11:20
URI: http://sro.sussex.ac.uk/id/eprint/50304
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