Fractals and Scaling in Finance

Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifica...

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Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applying ideas of scaling and self-similarity to arrays of data generated by financial analyses. This book brings together his original papers as well as many original chapters specifically written for this book.

List of Chapters
In this List of Chapters, the sources given after the titles include (in parentheses)
the letter M followed by the year of publication and by the lower case letter that the
Bibliography uses to distinguish different texts published in the same year. In the
Bibliography, the items reproduced in this book and in Volumes N and H are
marked by a star followed by a chapter number, which in some cases is incomplete
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List of Chapters
In this List of Chapters, the sources given after the titles include (in parentheses)
the letter M followed by the year of publication and by the lower case letter that the
Bibliography uses to distinguish different texts published in the same year. In the
Bibliography, the items reproduced in this book and in Volumes N and H are
marked by a star followed by a chapter number, which in some cases is incomplete
or only tentative.
Foreword by Ralph E. Gomory ix
I • NONMATHEMATICAL PRESENTATIONS
Preface (1996) 1
El Introduction (1996) 13
E2 Discontinuity and scaling: scope and
likely limitations (1996) 50
E3 New methods in statistical economics (M 1963e) 79
E4 Sources of inspiration and historical background (1996) 105
II • MATHEMATICAL PRESENTATIONS
E5 States of randomness from mild to wild, and
concentration in the short, medium and long run (1996) 117
E6 Self-similarity and panorama of self-affinity (1996) 146
E7 Rank-size plots, Zipf's law, and scaling (1996) 198
E8 Proportional growth with or without diffusion,
and other explanations of scaling (1996).
• Appendices (M 1964o, M 1974d) 219
E9 A case against the lognormal distribution (1996) 252
III • PERSONAL INCOMES AND FIRM SIZES
E10 L-stable model for the distribution of income (M 1960i).
• Appendices (M 1963i, M 1963j) 271
Ell L-stability and multiplicative variation of income (M 1961e) 307
E12 Scaling distributions and income maximization (M 1962q) 336
E13 Industrial concentration and scaling (1996) 364
IV • THE M 1963 MODEL OF PRICE VARIATION
E14 The variation of certain speculative prices (M 1963b).
• Appendices (Fama & Blume 1966, M 1972b, M 1982c) 371
E15 The variation of the price of cotton, wheat, and railroad
stocks, and of some financial rates (M 1967j) 419
E16 Mandelbrot on price variation (Fama 1963)
(A guest contribution by E. F. Fama) 444
El7 Comments by P. H. Cootner, E. Parzen & W. S. Morris
(1960s), and responses (1996) 458
E18 Computation of the L-stable distributions (1996) 466
V • BEYOND THE M 1963 MODEL
El9 Nonlinear forecasts, rational bubbles, and
martingales (M 1966b) 471
E20 Limitations of efficiency and martingales (M 1971e) 492
E21 Self-affine variation in fractal time
(Section 1 is by W. H. Taylor) (M & Taylor 1967, M 1973c) 513
CUMULATIVE BIBLIOGRAPHY 526
INDEX 542
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