Fractional calculus and continuous-time finance

Enrico Scalas, Rudolf Gorenflo and Francesco Mainardi

Physica A: Statistical Mechanics and its Applications, 2000, vol. 284, issue 1, 376-384

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; Econophysics (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (141)

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Related works:
Working Paper: Fractional calculus and continuous-time finance (2004)
Working Paper: Fractional calculus and continuous-time finance (2000)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:284:y:2000:i:1:p:376-384

DOI: 10.1016/S0378-4371(00)00255-7

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