文档介绍：INTRODUCTION TO THE SERIES
The Handbooks in Finance are intended to be a definitive source prehensive and
accessible information in the field of finance. Each individual volume in the series should
present an accurate self-contained survey of a sub-field of finance, suitable for use by
finance and economics professors and lecturers, professional researchers, graduate students
and as a teaching supplement. The goal is to have a broad group of outstanding volumes in
various areas of finance.
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Chapter 1
HEAVY TAILS IN FINANCE FOR INDEPENDENT
OR MULTIFRACTAL PRICE INCREMENTS
BENOIT B. MANDELBROT
Sterling Professor of Mathematical Sciences, Yale University, New Haven, CT 065020-8283, USA
Contents
Abstract 4
1. Introduction: A path that led to model price by Brownian motion (Wiener or
fractional) of a multifractal trading time 5
. From the law of Pareto to infinite moment “anomalies” that contradict the Gaussian “norm” 5
. A scientific principle: scaling invariance in finance 6
. Analysis alone versus statistical analysis followed by synthesis and graphic output 7
. Actual implementation of scaling invariance by multifractal functions: it requires additional
assumptions that are convenient but not a matter of principle, for example, separability and
compounding 7
2. Background: the Bernoulli binomial measure and two random variants: shuffled
and canonical 8
. Definition and construction of the Bernoulli binomial measure 8
. The concept of canonical random cascade and the definition of the canonical binomial measure 9
. Two forms of conservation: strict and on the average 9
. The term “canonical” is motivated by statistical thermodynamics 10
. In every variant of the binomial measure one can view all finite (positive or negative) powers
together, as forming a single “class of equivalence” 10
. The full and folded forms of the address plane 11
. Alternative parameters 11
3. Definition of the two-valued