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Fractional calculus and continuous-time finance

Enrico Scalas, Rudolf Gorenflo, Francesco Mainardi

posted on 01 January 2000

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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.