Fractional calculus and continuous-time finance

Enrico Scalas (), Rudolf Gorenflo and Francesco Mainardi
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Rudolf Gorenflo: Freie Universitaet Berlin, Berlin, Germany
Francesco Mainardi: Universita' di Bologna, Bologna, Italy

Finance from EconWPA

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 Lévy 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.

Keywords: Stochastic processes; random walk; statistical finance; duration (search for similar items in EconPapers)
JEL-codes: G (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets and nep-fin
Date: 2004-11-05
Note: Type of Document - pdf; pages: 11. Preprint pdf version of a paper published in Physica A, vol.284, p.376-384, 2000.
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Working Paper: Fractional calculus and continuous-time finance (2000)
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Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpfi:0411007

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