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Fractals and Scaling in Finance

Discontinuity, Concentration, Risk. Selecta Volume E

  • Book
  • © 1997

Overview

Authors:
  1. Benoit B. Mandelbrot

    1. Mathematics Department, Yale University, New Haven, USA

    View author publications

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  • Mandelbrot is a world renowned scientist and pioneer in fractal research.

  • However, his original field of applied research was in econometrics and financial models.

  • Contains new material prepared specifically for this volume, as well as reprints of his classic papers.

  • Much of this work helps to lay a foundation for evaluating risks in trading strategies.

  • Includes applicable real-life models such as random flight on Wall Street, personal incomes and firm sizes, etc.

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-12
    Download chapter 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
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About this book

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.

Reviews

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."

Authors and Affiliations

  • Mathematics Department, Yale University, New Haven, USA

    Benoit B. Mandelbrot

Bibliographic Information

  • Book Title: Fractals and Scaling in Finance

  • Book Subtitle: Discontinuity, Concentration, Risk. Selecta Volume E

  • Authors: Benoit B. Mandelbrot

  • DOI: https://doi.org/10.1007/978-1-4757-2763-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-98363-9Published: 18 September 1997

  • Softcover ISBN: 978-1-4419-3119-1Published: 01 December 2010

  • eBook ISBN: 978-1-4757-2763-0Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: X, 551

  • Topics: Quantitative Finance

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