Fractals and Scaling in Finance

1. Front Matter

   Pages i-12

   PDF

2. Nonmathematical Presentations

   1. Introduction

      • Benoit B. Mandelbrot

      Pages 13-49

   2. Discontinuity and scaling: their scope and likely limitations

      • Benoit B. Mandelbrot

      Pages 50-78

   3. New methods in statistical economics

      • Benoit B. Mandelbrot

      Pages 79-104

   4. Sources of inspiration and historical background

      • Benoit B. Mandelbrot

      Pages 105-116

3. Mathematical Presentations

   1. States of randomness from mild to wild, and concentration from the short to the long run

      • Benoit B. Mandelbrot

      Pages 117-145

   2. Self-similarity and panorama of self-affinity

      • Benoit B. Mandelbrot

      Pages 146-197

   3. Rank-size plots, Zipf’s law, and scaling

      • Benoit B. Mandelbrot

      Pages 198-218

   4. Proportional growth with or without diffusion, and other explanations of scaling

      • Benoit B. Mandelbrot

      Pages 219-251

   5. A case against the lognormal distribution

      • Benoit B. Mandelbrot

      Pages 252-269

4. Personal Incomes and Firms

   1. L-stable model for the distribution of income

      • Benoit B. Mandelbrot

      Pages 271-306

   2. L-stability and multiplicative variation of income

      • Benoit B. Mandelbrot

      Pages 307-335

   3. Scaling distributions and income maximization

      • Benoit B. Mandelbrot

      Pages 336-363

   4. Industrial concentration and scaling

      • Benoit B. Mandelbrot

      Pages 364-369

5. The 1963 Model of Price Change

   1. The variation of certain speculative prices

      • Benoit B. Mandelbrot

      Pages 371-418

   2. The variation of the prices of cotton, wheat, and railroad stocks, and of some financial rates

      • Benoit B. Mandelbrot

      Pages 419-443

   3. Mandelbrot on price variation

      • Benoit B. Mandelbrot

      Pages 444-457

   4. Comments by P. H. Cootner, E. Parzen, and W. S. Morris (1960s) and responses

      • Benoit B. Mandelbrot

      Pages 458-465

   5. Computation of the L-stable distributions

      • Benoit B. Mandelbrot

      Pages 466-469

6. Beyond the M 1963 Model

   1. Nonlinear forecasts, rational bubbles, and martingales

      • Benoit B. Mandelbrot

      Pages 471-491

IN 1959-61, while the huge Saarinen-designed research laboratory at Yorktown Heights was being built, much of IBM's Research was housed nearby. My group occupied one of the many little houses on the Lamb Estate complex which had been a sanatorium housing wealthy alcoholics. The picture below was taken about 1960. It shows from right to left, T. e. Hu, now at the University of California, Santa Barbara. I am next, staring at a network I have just written on the blackboard. Then comes Paul Gilmore, late of the University of British Columbia, then (seated) Richard Levitan, now retired, and at the left is Benoit Mandelbrot. x FOREWORD EF Even in a Lamb Estate populated exclusively with bright research­ oriented people, Benoit always stood out. His thinking was always fresh, and I enjoyed talking with him about any subject, whether technical, poli­ tical, or historical. He introduced me to the idea that distributions having infinite second moments could be more than a mathematical curiosity and a source of counter-examples. This was a foretaste of the line of thought that eventually led to fractals and to the notion that major pieces of the physical world could be, and in fact could only be, modeled by distrib­ utions and sets that had fractional dimensions. Usually these distributions and sets were known to mathematicians, as they were known to me, as curiosities and counter-intuitive examples used to show graduate students the need for rigor in their proofs.

• Excel
• econometrics
• efficiency
• fractal
• fractal geometry
• linear optimization
• mathematics
• normal distribution
• quantitative finance

From the reviews
"Mandelbrot writes with economy and felicity, and he interperses the more mathematical sections with frank historical anecdotes ... All in all, this is a strange but wonderful book." (PHYSICS TODAY)

Statistical Papers, 2000: "... this is a most useful collection of Mandelbrot's work economics, it provides an excellent starting point for anybody interested in the origin of many current topics in empirical finance or the distribution of income."

• Mathematics Department, Yale University, New Haven, USA

  Benoit B. Mandelbrot