Fractional calculus and continuous-time finance

Enrico Scalas, Rudolf Gorenflo and Francesco Mainardi

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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.

Date: 2000-01
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Citations: View citations in EconPapers (140)

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Working Paper: Fractional calculus and continuous-time finance (2004)
Journal Article: Fractional calculus and continuous-time finance (2000)
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