Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E

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Springer Science & Business Media, Mar 9, 2013 - Mathematics - 551 pages
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.
 

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Contents

Foreword by Ralph E Gomory
1
E1 Introduction 1996
13
scope
50
E3 New methods in statistical economics M 1963e
79
E4 Sources of inspiration and historical background 1996
105
MATHEMATICAL PRESENTATIONS
117
E6 Selfsimilarity and panorama of selfaffinity 1996
146
E7 Ranksize plots Zipfs law and scaling 1996
198
E12 Scaling distributions and income maximization M 1962q
336
E13 Industrial concentration and scaling 1996
364
e THE M 1963 MODEL OF PRICE VARIATION
371
E15 The variation of the price of cotton wheat and railroad
419
E16 Mandelbrot on price variation Fama 1963
444
E17 Comments by P H Cootner E Parzen W S Morris
458
E18 Computation of the Lstable distributions 1996
466
E20 Limitations of efficiency and martingales M 1971e
492

E8 Proportional growth with or without diffusion
219
E9 A case against the lognormal distribution 1996
252
E10 Lstable model for the distribution of income M 1960i
270
E11 Lstability and multiplicative variation of income M 1961e
307
E21 Selfaffine variation in fractal time
513
CUMULATIVE BIBLIOGRAPHY
526
INDEX
542
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