Abstract
Chapter E1 stated emphatically my view that Gaussianity, random walks and martingales are attractive hypotheses, but disagree with the evidence concerning price variation. This chapter presents, in largely non-mathematical style, the processes I propose as replacements for Brownian motion. Their foundations include an evidence-based theme and a conceptual tool.
The theme is discussed in Section 1: it is discontinuity and the related notions of concentration and cyclicity. The tool, scaling, is discussed in Section 2. The possible limitations of scaling expressed by cutoffs and crossovers are discussed in Section 3. Section 4 comments on alternative approaches that contradict scaling, and instead replace Brownian motion by a “patchwork” of step-by-step “fixes.” Section 5 describes some paradoxes of scaling.
Stationarity and scaling express invariances with respect to translation in time and change in the unit of time. Diverse principles of invariance are essential to my work, in economics as well as in physics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mandelbrot, B.B. (1997). Discontinuity and scaling: their scope and likely limitations. In: Fractals and Scaling in Finance. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2763-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2763-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3119-1
Online ISBN: 978-1-4757-2763-0
eBook Packages: Springer Book Archive