Fractals and Scaling in Finance

by Mandelbrot, Benoit B.

• ISBN13: 9780387983639
• ISBN10: 0387983635
• Format: Hardcover
• Copyright: 1997-10-01
• Publisher: Springer Verlag

Summary

This is the first book in the Selecta, the collected works of Benoit Mandelbrot. This volume incorporates his original contributions to finance and is a major contribution to the understanding of how speculative prices vary in time. The chapters consist of much new material prepared 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. 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."

Table of Contents

Foreword	ix
Ralph E. Gomory
I NONMATHEMATICAL PRESENTATIONS	1	(116)
Preface (1996)	1	(12)
E1 Introduction (1996)	13	(37)
E2 Discontinuity and scaling: scope and likely limitations (1996)	50	(29)
E3 New methods in statistical economics (M 1963e)	79	(26)
E4 Sources of inspiration and historical background (1996)	105	(12)
II MATHEMATICAL PRESENTATIONS	117	(154)
E5 States of randomness from mild to wild, and concentration in the short, medium and long run (1996)	117	(29)
E6 Self-similarity and panorama of self-affinity (1996)	146	(52)
E7 Rank-size plots, Zipf's law, and scaling (1996)	198	(21)
E8 Proportional growth with or without diffusion, and other explanations of scaling (1996) Appendices (M 1964o, M 1974d)	219	(33)
E9 A case against the lognormal distribution (1996)	252	(19)
III PERSONAL INCOMES AND FIRM SIZES	271	(100)
E10 L-stable model for the distribution of income (M 1960i) Appendices (M 1963i, M 1963j)	271	(36)
E11 L-stability and multiplicative variation of income (M 1961e)	307	(29)
E12 Scaling distributions and income maximization (M 1962q)	336	(28)
E13 Industrial concentration and scaling (1996)	364	(7)
IV THE M 1963 MODEL OF PRICE VARIATION	371	(100)
E14 The variation of certain speculative prices (M 1963b) Appendices (Fama & Blume 1966, M 1972b, M 1982c)	371	(48)
E15 The variation of the price of cotton, wheat, and railroad stocks, and of some financial rates (M 1967j)	419	(25)
E16 Mandelbrot on price variation (Fama 1963) (A guest contribution by E. F. Fama)	444	(14)
E17 Comments by P. H. Cootner, E. Parzen & W. S. Morris (1960s), and responses (1996)	458	(8)
E18 Computation of the L-stable distributions (1996)	466	(5)
V BEYOND THE M 1963 MODEL	471	(55)
E19 Nonlinear forecasts, rational bubbles, and martingales (M 1966b)	471	(21)
E20 Limitations of efficiency and martingales (M 1971e)	492	(21)
E21 Self-affine variation in fractal time (Section 1 is by W. H. Taylor) (M & Taylor 1967, M 1973c)	513	(13)
CUMULATIVE BIBLIOGRAPHY	526	(16)
INDEX	542