TY - JOUR
T1 - Fractional calculus and continuous-time finance
AU - Scalas, Enrico
AU - Gorenflo, Rudolf
AU - Mainardi, Francesco
N1 - Funding Information:
This work was partially supported by the Italian INFM and INFN, and by the Research Commission of the Free University in Berlin. R.G. is grateful to the Italian “Istituto Nazionale di Alta Matematica”, for supporting his visit in Italy. E.S. wishes to thank CERN for its wonderful library which is open 24 h a day: an ideal place to study in a quiet atmosphere after shifts at the colliders. Discussions on high-frequency financial data with Marco Raberto inspired this work. Last but not the least, we wish to thank the referee, who pointed us to a very relevant piece of literature ( Ref. [22] ) of which we were not aware.
PY - 2000/9/1
Y1 - 2000/9/1
N2 - 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 Levy 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.
AB - 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 Levy 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.
UR - https://www.scopus.com/pages/publications/0034275979
U2 - 10.1016/S0378-4371(00)00255-7
DO - 10.1016/S0378-4371(00)00255-7
M3 - Article
SN - 0378-4371
VL - 284
SP - 376
EP - 384
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1
ER -