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Fractional calculus and continuous-time finance

Enrico Scalas·Rudolf Gorenflo·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 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.

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Enrico Scalas, Rudolf Gorenflo, Francesco Mainardi. 2000-01-10. Fractional calculus and continuous-time finance. https://doi.org/10.1016/s0378-4371(00)00255-7

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