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Fractional calculus and continuous-time finance

Author

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  • Scalas, Enrico
  • Gorenflo, Rudolf
  • Mainardi, Francesco

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.

Suggested Citation

  • Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    • Handle: RePEc:eee:phsmap:v:284:y:2000:i:1:p:376-384
    DOI: 10.1016/S0378-4371(00)00255-7
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