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Fractional calculus and continuous-time finance. III: The diffusion limit. (English) Zbl 1138.91444

Kohlmann, Michael (ed.) et al., Mathematical finance. Workshop of the mathematical finance research project, Konstanz, Germany, October 5–7, 2000. Basel: Birkhäuser (ISBN 3-7643-6553-6). 171-180 (2001).
Summary: We complement the theory of tick-by-tick dynamics of financial markets based on a continuous-time random walk (CTRW) model recently proposed by Scalas et al. [Physica A 284, No. 1-4, 376–384 (2000)], and we point out its consistency with the behaviour observed in the waiting-time distribution for BUND future prices traded at LIFFE, London.
In Part I (loc. cit.), we presented 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 was given, based on the solution of the fractional diffusion equation.
For the entire collection see [Zbl 0964.00056].

MSC:

91B28 Finance etc. (MSC2000)
60J60 Diffusion processes
91B62 Economic growth models
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